linear_algebra.matrix.trace | Mathlib porting status

Changes since the initial port

The following section lists changes to this file in mathlib3 and mathlib4 that occured after the initial port. Most recent changes are shown first. Hovering over a commit will show all commits associated with the same mathlib3 commit.

Changes in mathlib3

32b08ef8

(last sync)

Changes in mathlib3port

mathlib3

mathlib3port

d64d67d0

bump to nightly-2023-09-24-06

mathlib commit https://github.com/leanprover-community/mathlib/commit/ce64cd319bb6b3e82f31c2d38e79080d377be451

5655435f

Diff

@@ -3,7 +3,7 @@ Copyright (c) 2019 Johannes Hölzl. All rights reserved.
 Released under Apache 2.0 license as described in the file LICENSE.
 Authors: Johannes Hölzl, Patrick Massot, Casper Putz, Anne Baanen
 -/
-import Mathbin.Data.Matrix.Basic
+import Data.Matrix.Basic
 
 #align_import linear_algebra.matrix.trace from "leanprover-community/mathlib"@"d64d67d000b974f0d86a2be7918cf800be6271c8"

d64d67d0

bump to nightly-2023-07-20-09

mathlib commit https://github.com/leanprover-community/mathlib/commit/8ea5598db6caeddde6cb734aa179cc2408dbd345

9c56d0dd

Diff

@@ -2,14 +2,11 @@
 Copyright (c) 2019 Johannes Hölzl. All rights reserved.
 Released under Apache 2.0 license as described in the file LICENSE.
 Authors: Johannes Hölzl, Patrick Massot, Casper Putz, Anne Baanen
-
-! This file was ported from Lean 3 source module linear_algebra.matrix.trace
-! leanprover-community/mathlib commit d64d67d000b974f0d86a2be7918cf800be6271c8
-! Please do not edit these lines, except to modify the commit id
-! if you have ported upstream changes.
 -/
 import Mathbin.Data.Matrix.Basic
 
+#align_import linear_algebra.matrix.trace from "leanprover-community/mathlib"@"d64d67d000b974f0d86a2be7918cf800be6271c8"
+
 /-!
 # Trace of a matrix

d64d67d0

bump to nightly-2023-06-13-21

mathlib commit https://github.com/leanprover-community/mathlib/commit/9fb8964792b4237dac6200193a0d533f1b3f7423

829520ac

Diff

@@ -52,28 +52,36 @@ def trace (A : Matrix n n R) : R :=
 
 variable (n R)
 
+#print Matrix.trace_zero /-
 @[simp]
 theorem trace_zero : trace (0 : Matrix n n R) = 0 :=
   (Finset.sum_const (0 : R)).trans <| smul_zero _
 #align matrix.trace_zero Matrix.trace_zero
+-/
 
 variable {n R}
 
+#print Matrix.trace_add /-
 @[simp]
 theorem trace_add (A B : Matrix n n R) : trace (A + B) = trace A + trace B :=
   Finset.sum_add_distrib
 #align matrix.trace_add Matrix.trace_add
+-/
 
+#print Matrix.trace_smul /-
 @[simp]
 theorem trace_smul [Monoid α] [DistribMulAction α R] (r : α) (A : Matrix n n R) :
     trace (r • A) = r • trace A :=
   Finset.smul_sum.symm
 #align matrix.trace_smul Matrix.trace_smul
+-/
 
+#print Matrix.trace_transpose /-
 @[simp]
 theorem trace_transpose (A : Matrix n n R) : trace Aᵀ = trace A :=
   rfl
 #align matrix.trace_transpose Matrix.trace_transpose
+-/
 
 #print Matrix.trace_conjTranspose /-
 @[simp]
@@ -108,10 +116,12 @@ def traceLinearMap [Semiring α] [Module α R] : Matrix n n R →ₗ[α] R
 
 variable {n α R}
 
+#print Matrix.trace_list_sum /-
 @[simp]
 theorem trace_list_sum (l : List (Matrix n n R)) : trace l.Sum = (l.map trace).Sum :=
   map_list_sum (traceAddMonoidHom n R) l
 #align matrix.trace_list_sum Matrix.trace_list_sum
+-/
 
 #print Matrix.trace_multiset_sum /-
 @[simp]
@@ -120,11 +130,13 @@ theorem trace_multiset_sum (s : Multiset (Matrix n n R)) : trace s.Sum = (s.map
 #align matrix.trace_multiset_sum Matrix.trace_multiset_sum
 -/
 
+#print Matrix.trace_sum /-
 @[simp]
 theorem trace_sum (s : Finset ι) (f : ι → Matrix n n R) :
     trace (∑ i in s, f i) = ∑ i in s, trace (f i) :=
   map_sum (traceAddMonoidHom n R) f s
 #align matrix.trace_sum Matrix.trace_sum
+-/
 
 end AddCommMonoid
 
@@ -132,15 +144,19 @@ section AddCommGroup
 
 variable [AddCommGroup R]
 
+#print Matrix.trace_sub /-
 @[simp]
 theorem trace_sub (A B : Matrix n n R) : trace (A - B) = trace A - trace B :=
   Finset.sum_sub_distrib
 #align matrix.trace_sub Matrix.trace_sub
+-/
 
+#print Matrix.trace_neg /-
 @[simp]
 theorem trace_neg (A : Matrix n n R) : trace (-A) = -trace A :=
   Finset.sum_neg_distrib
 #align matrix.trace_neg Matrix.trace_neg
+-/
 
 end AddCommGroup
 
@@ -148,39 +164,51 @@ section One
 
 variable [DecidableEq n] [AddCommMonoidWithOne R]
 
+#print Matrix.trace_one /-
 @[simp]
 theorem trace_one : trace (1 : Matrix n n R) = Fintype.card n := by
   simp_rw [trace, diag_one, Pi.one_def, Finset.sum_const, nsmul_one, Finset.card_univ]
 #align matrix.trace_one Matrix.trace_one
+-/
 
 end One
 
 section Mul
 
+#print Matrix.trace_transpose_mul /-
 @[simp]
 theorem trace_transpose_mul [AddCommMonoid R] [Mul R] (A : Matrix m n R) (B : Matrix n m R) :
     trace (Aᵀ ⬝ Bᵀ) = trace (A ⬝ B) :=
   Finset.sum_comm
 #align matrix.trace_transpose_mul Matrix.trace_transpose_mul
+-/
 
+#print Matrix.trace_mul_comm /-
 theorem trace_mul_comm [AddCommMonoid R] [CommSemigroup R] (A : Matrix m n R) (B : Matrix n m R) :
     trace (A ⬝ B) = trace (B ⬝ A) := by rw [← trace_transpose, ← trace_transpose_mul, transpose_mul]
 #align matrix.trace_mul_comm Matrix.trace_mul_comm
+-/
 
+#print Matrix.trace_mul_cycle /-
 theorem trace_mul_cycle [NonUnitalCommSemiring R] (A : Matrix m n R) (B : Matrix n p R)
     (C : Matrix p m R) : trace (A ⬝ B ⬝ C) = trace (C ⬝ A ⬝ B) := by
   rw [trace_mul_comm, Matrix.mul_assoc]
 #align matrix.trace_mul_cycle Matrix.trace_mul_cycle
+-/
 
+#print Matrix.trace_mul_cycle' /-
 theorem trace_mul_cycle' [NonUnitalCommSemiring R] (A : Matrix m n R) (B : Matrix n p R)
     (C : Matrix p m R) : trace (A ⬝ (B ⬝ C)) = trace (C ⬝ (A ⬝ B)) := by
   rw [← Matrix.mul_assoc, trace_mul_comm]
 #align matrix.trace_mul_cycle' Matrix.trace_mul_cycle'
+-/
 
+#print Matrix.trace_col_mul_row /-
 @[simp]
 theorem trace_col_mul_row [NonUnitalNonAssocSemiring R] (a b : n → R) :
     trace (col a ⬝ row b) = dotProduct a b := by simp [dot_product, trace]
 #align matrix.trace_col_mul_row Matrix.trace_col_mul_row
+-/
 
 end Mul
 
@@ -195,22 +223,30 @@ with `matrix.det_fin_two` etc.
 -/
 
 
+#print Matrix.trace_fin_zero /-
 @[simp]
 theorem trace_fin_zero (A : Matrix (Fin 0) (Fin 0) R) : trace A = 0 :=
   rfl
 #align matrix.trace_fin_zero Matrix.trace_fin_zero
+-/
 
+#print Matrix.trace_fin_one /-
 theorem trace_fin_one (A : Matrix (Fin 1) (Fin 1) R) : trace A = A 0 0 :=
   add_zero _
 #align matrix.trace_fin_one Matrix.trace_fin_one
+-/
 
+#print Matrix.trace_fin_two /-
 theorem trace_fin_two (A : Matrix (Fin 2) (Fin 2) R) : trace A = A 0 0 + A 1 1 :=
   congr_arg ((· + ·) _) (add_zero (A 1 1))
 #align matrix.trace_fin_two Matrix.trace_fin_two
+-/
 
+#print Matrix.trace_fin_three /-
 theorem trace_fin_three (A : Matrix (Fin 3) (Fin 3) R) : trace A = A 0 0 + A 1 1 + A 2 2 := by
   rw [← add_zero (A 2 2), add_assoc]; rfl
 #align matrix.trace_fin_three Matrix.trace_fin_three
+-/
 
 end Fin

d64d67d0

bump to nightly-2023-05-28-18

mathlib commit https://github.com/leanprover-community/mathlib/commit/917c3c072e487b3cccdbfeff17e75b40e45f66cb

8d353152

Diff

@@ -28,7 +28,7 @@ matrix, trace, diagonal
 -/
 
 
-open BigOperators Matrix
+open scoped BigOperators Matrix
 
 namespace Matrix

d64d67d0

bump to nightly-2023-05-28-06

mathlib commit https://github.com/leanprover-community/mathlib/commit/917c3c072e487b3cccdbfeff17e75b40e45f66cb

ba5d8b97

Diff

@@ -52,12 +52,6 @@ def trace (A : Matrix n n R) : R :=
 
 variable (n R)
 
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-Case conversion may be inaccurate. Consider using '#align matrix.trace_zero Matrix.trace_zeroₓ'. -/
 @[simp]
 theorem trace_zero : trace (0 : Matrix n n R) = 0 :=
   (Finset.sum_const (0 : R)).trans <| smul_zero _
@@ -65,35 +59,17 @@ theorem trace_zero : trace (0 : Matrix n n R) = 0 :=
 
 variable {n R}
 
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-Case conversion may be inaccurate. Consider using '#align matrix.trace_add Matrix.trace_addₓ'. -/
 @[simp]
 theorem trace_add (A B : Matrix n n R) : trace (A + B) = trace A + trace B :=
   Finset.sum_add_distrib
 #align matrix.trace_add Matrix.trace_add
 
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-Case conversion may be inaccurate. Consider using '#align matrix.trace_smul Matrix.trace_smulₓ'. -/
 @[simp]
 theorem trace_smul [Monoid α] [DistribMulAction α R] (r : α) (A : Matrix n n R) :
     trace (r • A) = r • trace A :=
   Finset.smul_sum.symm
 #align matrix.trace_smul Matrix.trace_smul
 
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-Case conversion may be inaccurate. Consider using '#align matrix.trace_transpose Matrix.trace_transposeₓ'. -/
 @[simp]
 theorem trace_transpose (A : Matrix n n R) : trace Aᵀ = trace A :=
   rfl
@@ -132,12 +108,6 @@ def traceLinearMap [Semiring α] [Module α R] : Matrix n n R →ₗ[α] R
 
 variable {n α R}
 
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-Case conversion may be inaccurate. Consider using '#align matrix.trace_list_sum Matrix.trace_list_sumₓ'. -/
 @[simp]
 theorem trace_list_sum (l : List (Matrix n n R)) : trace l.Sum = (l.map trace).Sum :=
   map_list_sum (traceAddMonoidHom n R) l
@@ -150,12 +120,6 @@ theorem trace_multiset_sum (s : Multiset (Matrix n n R)) : trace s.Sum = (s.map
 #align matrix.trace_multiset_sum Matrix.trace_multiset_sum
 -/
 
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 @[simp]
 theorem trace_sum (s : Finset ι) (f : ι → Matrix n n R) :
     trace (∑ i in s, f i) = ∑ i in s, trace (f i) :=
@@ -168,23 +132,11 @@ section AddCommGroup
 
 variable [AddCommGroup R]
 
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 @[simp]
 theorem trace_sub (A B : Matrix n n R) : trace (A - B) = trace A - trace B :=
   Finset.sum_sub_distrib
 #align matrix.trace_sub Matrix.trace_sub
 
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 @[simp]
 theorem trace_neg (A : Matrix n n R) : trace (-A) = -trace A :=
   Finset.sum_neg_distrib
@@ -196,12 +148,6 @@ section One
 
 variable [DecidableEq n] [AddCommMonoidWithOne R]
 
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 @[simp]
 theorem trace_one : trace (1 : Matrix n n R) = Fintype.card n := by
   simp_rw [trace, diag_one, Pi.one_def, Finset.sum_const, nsmul_one, Finset.card_univ]
@@ -211,56 +157,26 @@ end One
 
 section Mul
 
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 @[simp]
 theorem trace_transpose_mul [AddCommMonoid R] [Mul R] (A : Matrix m n R) (B : Matrix n m R) :
     trace (Aᵀ ⬝ Bᵀ) = trace (A ⬝ B) :=
   Finset.sum_comm
 #align matrix.trace_transpose_mul Matrix.trace_transpose_mul
 
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 theorem trace_mul_comm [AddCommMonoid R] [CommSemigroup R] (A : Matrix m n R) (B : Matrix n m R) :
     trace (A ⬝ B) = trace (B ⬝ A) := by rw [← trace_transpose, ← trace_transpose_mul, transpose_mul]
 #align matrix.trace_mul_comm Matrix.trace_mul_comm
 
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 theorem trace_mul_cycle [NonUnitalCommSemiring R] (A : Matrix m n R) (B : Matrix n p R)
     (C : Matrix p m R) : trace (A ⬝ B ⬝ C) = trace (C ⬝ A ⬝ B) := by
   rw [trace_mul_comm, Matrix.mul_assoc]
 #align matrix.trace_mul_cycle Matrix.trace_mul_cycle
 
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 theorem trace_mul_cycle' [NonUnitalCommSemiring R] (A : Matrix m n R) (B : Matrix n p R)
     (C : Matrix p m R) : trace (A ⬝ (B ⬝ C)) = trace (C ⬝ (A ⬝ B)) := by
   rw [← Matrix.mul_assoc, trace_mul_comm]
 #align matrix.trace_mul_cycle' Matrix.trace_mul_cycle'
 
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 @[simp]
 theorem trace_col_mul_row [NonUnitalNonAssocSemiring R] (a b : n → R) :
     trace (col a ⬝ row b) = dotProduct a b := by simp [dot_product, trace]
@@ -279,43 +195,19 @@ with `matrix.det_fin_two` etc.
 -/
 
 
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 @[simp]
 theorem trace_fin_zero (A : Matrix (Fin 0) (Fin 0) R) : trace A = 0 :=
   rfl
 #align matrix.trace_fin_zero Matrix.trace_fin_zero
 
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 theorem trace_fin_one (A : Matrix (Fin 1) (Fin 1) R) : trace A = A 0 0 :=
   add_zero _
 #align matrix.trace_fin_one Matrix.trace_fin_one
 
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 theorem trace_fin_two (A : Matrix (Fin 2) (Fin 2) R) : trace A = A 0 0 + A 1 1 :=
   congr_arg ((· + ·) _) (add_zero (A 1 1))
 #align matrix.trace_fin_two Matrix.trace_fin_two
 
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(OrderedSemiring.zeroLEOneClass.{0} Nat Nat.orderedSemiring) (NeZero.one.{0} Nat (NonAssocSemiring.toMulZeroOneClass.{0} Nat (Semiring.toNonAssocSemiring.{0} Nat Nat.semiring)) Nat.nontrivial) (OrderedAddCommMonoid.to_covariantClass_left.{0} Nat (OrderedSemiring.toOrderedAddCommMonoid.{0} Nat Nat.orderedSemiring))))))))))
-but is expected to have type
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-Case conversion may be inaccurate. Consider using '#align matrix.trace_fin_three Matrix.trace_fin_threeₓ'. -/
 theorem trace_fin_three (A : Matrix (Fin 3) (Fin 3) R) : trace A = A 0 0 + A 1 1 + A 2 2 := by
   rw [← add_zero (A 2 2), add_assoc]; rfl
 #align matrix.trace_fin_three Matrix.trace_fin_three

d64d67d0

bump to nightly-2023-05-28-04

mathlib commit https://github.com/leanprover-community/mathlib/commit/917c3c072e487b3cccdbfeff17e75b40e45f66cb

6797a637

Diff

@@ -316,10 +316,8 @@ lean 3 declaration is
 but is expected to have type
   forall {R : Type.{u1}} [_inst_4 : AddCommMonoid.{u1} R] (A : Matrix.{0, 0, u1} (Fin (OfNat.ofNat.{0} Nat 3 (instOfNatNat 3))) (Fin (OfNat.ofNat.{0} Nat 3 (instOfNatNat 3))) R), Eq.{succ u1} R (Matrix.trace.{0, u1} (Fin (OfNat.ofNat.{0} Nat 3 (instOfNatNat 3))) R (Fin.fintype (OfNat.ofNat.{0} Nat 3 (instOfNatNat 3))) _inst_4 A) (HAdd.hAdd.{u1, u1, u1} R R R (instHAdd.{u1} R (AddZeroClass.toAdd.{u1} R (AddMonoid.toAddZeroClass.{u1} R (AddCommMonoid.toAddMonoid.{u1} R _inst_4)))) (HAdd.hAdd.{u1, u1, u1} R R R (instHAdd.{u1} R (AddZeroClass.toAdd.{u1} R (AddMonoid.toAddZeroClass.{u1} R (AddCommMonoid.toAddMonoid.{u1} R _inst_4)))) (A (OfNat.ofNat.{0} (Fin (OfNat.ofNat.{0} Nat 3 (instOfNatNat 3))) 0 (Fin.instOfNatFin (OfNat.ofNat.{0} Nat 3 (instOfNatNat 3)) 0 (NeZero.succ (OfNat.ofNat.{0} Nat 2 (instOfNatNat 2))))) (OfNat.ofNat.{0} (Fin (OfNat.ofNat.{0} Nat 3 (instOfNatNat 3))) 0 (Fin.instOfNatFin (OfNat.ofNat.{0} Nat 3 (instOfNatNat 3)) 0 (NeZero.succ (OfNat.ofNat.{0} Nat 2 (instOfNatNat 2)))))) (A (OfNat.ofNat.{0} (Fin (OfNat.ofNat.{0} Nat 3 (instOfNatNat 3))) 1 (Fin.instOfNatFin (OfNat.ofNat.{0} Nat 3 (instOfNatNat 3)) 1 (NeZero.succ (OfNat.ofNat.{0} Nat 2 (instOfNatNat 2))))) (OfNat.ofNat.{0} (Fin (OfNat.ofNat.{0} Nat 3 (instOfNatNat 3))) 1 (Fin.instOfNatFin (OfNat.ofNat.{0} Nat 3 (instOfNatNat 3)) 1 (NeZero.succ (OfNat.ofNat.{0} Nat 2 (instOfNatNat 2))))))) (A (OfNat.ofNat.{0} (Fin (OfNat.ofNat.{0} Nat 3 (instOfNatNat 3))) 2 (Fin.instOfNatFin (OfNat.ofNat.{0} Nat 3 (instOfNatNat 3)) 2 (NeZero.succ (OfNat.ofNat.{0} Nat 2 (instOfNatNat 2))))) (OfNat.ofNat.{0} (Fin (OfNat.ofNat.{0} Nat 3 (instOfNatNat 3))) 2 (Fin.instOfNatFin (OfNat.ofNat.{0} Nat 3 (instOfNatNat 3)) 2 (NeZero.succ (OfNat.ofNat.{0} Nat 2 (instOfNatNat 2)))))))
 Case conversion may be inaccurate. Consider using '#align matrix.trace_fin_three Matrix.trace_fin_threeₓ'. -/
-theorem trace_fin_three (A : Matrix (Fin 3) (Fin 3) R) : trace A = A 0 0 + A 1 1 + A 2 2 :=
-  by
-  rw [← add_zero (A 2 2), add_assoc]
-  rfl
+theorem trace_fin_three (A : Matrix (Fin 3) (Fin 3) R) : trace A = A 0 0 + A 1 1 + A 2 2 := by
+  rw [← add_zero (A 2 2), add_assoc]; rfl
 #align matrix.trace_fin_three Matrix.trace_fin_three
 
 end Fin

d64d67d0

bump to nightly-2023-04-06-02

mathlib commit https://github.com/leanprover-community/mathlib/commit/06a655b5fcfbda03502f9158bbf6c0f1400886f9

89485060

Diff

@@ -4,7 +4,7 @@ Released under Apache 2.0 license as described in the file LICENSE.
 Authors: Johannes Hölzl, Patrick Massot, Casper Putz, Anne Baanen
 
 ! This file was ported from Lean 3 source module linear_algebra.matrix.trace
-! leanprover-community/mathlib commit 32b08ef840dd25ca2e47e035c5da03ce16d2dc3c
+! leanprover-community/mathlib commit d64d67d000b974f0d86a2be7918cf800be6271c8
 ! Please do not edit these lines, except to modify the commit id
 ! if you have ported upstream changes.
 -/
@@ -13,6 +13,9 @@ import Mathbin.Data.Matrix.Basic
 /-!
 # Trace of a matrix
 
+> THIS FILE IS SYNCHRONIZED WITH MATHLIB4.
+> Any changes to this file require a corresponding PR to mathlib4.
+
 This file defines the trace of a matrix, the map sending a matrix to the sum of its diagonal
 entries.

32b08ef8

bump to nightly-2023-04-03-02

mathlib commit https://github.com/leanprover-community/mathlib/commit/d95bef0d215ea58c0fd7bbc4b151bf3fe952c095

8477bcac

Diff

@@ -37,6 +37,7 @@ section AddCommMonoid
 
 variable [AddCommMonoid R]
 
+#print Matrix.trace /-
 /-- The trace of a square matrix. For more bundled versions, see:
 * `matrix.trace_add_monoid_hom`
 * `matrix.trace_linear_map`
@@ -44,9 +45,16 @@ variable [AddCommMonoid R]
 def trace (A : Matrix n n R) : R :=
   ∑ i, diag A i
 #align matrix.trace Matrix.trace
+-/
 
 variable (n R)
 
+/- warning: matrix.trace_zero -> Matrix.trace_zero is a dubious translation:
+lean 3 declaration is
+  forall (n : Type.{u1}) (R : Type.{u2}) [_inst_2 : Fintype.{u1} n] [_inst_4 : AddCommMonoid.{u2} R], Eq.{succ u2} R (Matrix.trace.{u1, u2} n R _inst_2 _inst_4 (OfNat.ofNat.{max u1 u2} (Matrix.{u1, u1, u2} n n R) 0 (OfNat.mk.{max u1 u2} (Matrix.{u1, u1, u2} n n R) 0 (Zero.zero.{max u1 u2} (Matrix.{u1, u1, u2} n n R) (Matrix.hasZero.{u2, u1, u1} n n R (AddZeroClass.toHasZero.{u2} R (AddMonoid.toAddZeroClass.{u2} R (AddCommMonoid.toAddMonoid.{u2} R _inst_4)))))))) (OfNat.ofNat.{u2} R 0 (OfNat.mk.{u2} R 0 (Zero.zero.{u2} R (AddZeroClass.toHasZero.{u2} R (AddMonoid.toAddZeroClass.{u2} R (AddCommMonoid.toAddMonoid.{u2} R _inst_4))))))
+but is expected to have type
+  forall (n : Type.{u1}) (R : Type.{u2}) [_inst_2 : Fintype.{u1} n] [_inst_4 : AddCommMonoid.{u2} R], Eq.{succ u2} R (Matrix.trace.{u1, u2} n R _inst_2 _inst_4 (OfNat.ofNat.{max u1 u2} (Matrix.{u1, u1, u2} n n R) 0 (Zero.toOfNat0.{max u1 u2} (Matrix.{u1, u1, u2} n n R) (Matrix.zero.{u2, u1, u1} n n R (AddMonoid.toZero.{u2} R (AddCommMonoid.toAddMonoid.{u2} R _inst_4)))))) (OfNat.ofNat.{u2} R 0 (Zero.toOfNat0.{u2} R (AddMonoid.toZero.{u2} R (AddCommMonoid.toAddMonoid.{u2} R _inst_4))))
+Case conversion may be inaccurate. Consider using '#align matrix.trace_zero Matrix.trace_zeroₓ'. -/
 @[simp]
 theorem trace_zero : trace (0 : Matrix n n R) = 0 :=
   (Finset.sum_const (0 : R)).trans <| smul_zero _
@@ -54,29 +62,50 @@ theorem trace_zero : trace (0 : Matrix n n R) = 0 :=
 
 variable {n R}
 
+/- warning: matrix.trace_add -> Matrix.trace_add is a dubious translation:
+lean 3 declaration is
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+but is expected to have type
+  forall {n : Type.{u2}} {R : Type.{u1}} [_inst_2 : Fintype.{u2} n] [_inst_4 : AddCommMonoid.{u1} R] (A : Matrix.{u2, u2, u1} n n R) (B : Matrix.{u2, u2, u1} n n R), Eq.{succ u1} R (Matrix.trace.{u2, u1} n R _inst_2 _inst_4 (HAdd.hAdd.{max u2 u1, max u2 u1, max u2 u1} (Matrix.{u2, u2, u1} n n R) (Matrix.{u2, u2, u1} n n R) (Matrix.{u2, u2, u1} n n R) (instHAdd.{max u2 u1} (Matrix.{u2, u2, u1} n n R) (Matrix.add.{u1, u2, u2} n n R (AddZeroClass.toAdd.{u1} R (AddMonoid.toAddZeroClass.{u1} R (AddCommMonoid.toAddMonoid.{u1} R _inst_4))))) A B)) (HAdd.hAdd.{u1, u1, u1} R R R (instHAdd.{u1} R (AddZeroClass.toAdd.{u1} R (AddMonoid.toAddZeroClass.{u1} R (AddCommMonoid.toAddMonoid.{u1} R _inst_4)))) (Matrix.trace.{u2, u1} n R _inst_2 _inst_4 A) (Matrix.trace.{u2, u1} n R _inst_2 _inst_4 B))
+Case conversion may be inaccurate. Consider using '#align matrix.trace_add Matrix.trace_addₓ'. -/
 @[simp]
 theorem trace_add (A B : Matrix n n R) : trace (A + B) = trace A + trace B :=
   Finset.sum_add_distrib
 #align matrix.trace_add Matrix.trace_add
 
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+  forall {n : Type.{u1}} {α : Type.{u2}} {R : Type.{u3}} [_inst_2 : Fintype.{u1} n] [_inst_4 : AddCommMonoid.{u3} R] [_inst_5 : Monoid.{u2} α] [_inst_6 : DistribMulAction.{u2, u3} α R _inst_5 (AddCommMonoid.toAddMonoid.{u3} R _inst_4)] (r : α) (A : Matrix.{u1, u1, u3} n n R), Eq.{succ u3} R (Matrix.trace.{u1, u3} n R _inst_2 _inst_4 (SMul.smul.{u2, max u1 u3} α (Matrix.{u1, u1, u3} n n R) (Matrix.hasSmul.{u3, u1, u1, u2} n n α R (SMulZeroClass.toHasSmul.{u2, u3} α R (AddZeroClass.toHasZero.{u3} R (AddMonoid.toAddZeroClass.{u3} R (AddCommMonoid.toAddMonoid.{u3} R _inst_4))) (DistribSMul.toSmulZeroClass.{u2, u3} α R (AddMonoid.toAddZeroClass.{u3} R (AddCommMonoid.toAddMonoid.{u3} R _inst_4)) (DistribMulAction.toDistribSMul.{u2, u3} α R _inst_5 (AddCommMonoid.toAddMonoid.{u3} R _inst_4) _inst_6)))) r A)) (SMul.smul.{u2, u3} α R (SMulZeroClass.toHasSmul.{u2, u3} α R (AddZeroClass.toHasZero.{u3} R (AddMonoid.toAddZeroClass.{u3} R (AddCommMonoid.toAddMonoid.{u3} R _inst_4))) (DistribSMul.toSmulZeroClass.{u2, u3} α R (AddMonoid.toAddZeroClass.{u3} R (AddCommMonoid.toAddMonoid.{u3} R _inst_4)) (DistribMulAction.toDistribSMul.{u2, u3} α R _inst_5 (AddCommMonoid.toAddMonoid.{u3} R _inst_4) _inst_6))) r (Matrix.trace.{u1, u3} n R _inst_2 _inst_4 A))
+but is expected to have type
+  forall {n : Type.{u1}} {α : Type.{u3}} {R : Type.{u2}} [_inst_2 : Fintype.{u1} n] [_inst_4 : AddCommMonoid.{u2} R] [_inst_5 : Monoid.{u3} α] [_inst_6 : DistribMulAction.{u3, u2} α R _inst_5 (AddCommMonoid.toAddMonoid.{u2} R _inst_4)] (r : α) (A : Matrix.{u1, u1, u2} n n R), Eq.{succ u2} R (Matrix.trace.{u1, u2} n R _inst_2 _inst_4 (HSMul.hSMul.{u3, max u1 u2, max u1 u2} α (Matrix.{u1, u1, u2} n n R) (Matrix.{u1, u1, u2} n n R) (instHSMul.{u3, max u1 u2} α (Matrix.{u1, u1, u2} n n R) (Matrix.smul.{u2, u1, u1, u3} n n α R (SMulZeroClass.toSMul.{u3, u2} α R (AddMonoid.toZero.{u2} R (AddCommMonoid.toAddMonoid.{u2} R _inst_4)) (DistribSMul.toSMulZeroClass.{u3, u2} α R (AddMonoid.toAddZeroClass.{u2} R (AddCommMonoid.toAddMonoid.{u2} R _inst_4)) (DistribMulAction.toDistribSMul.{u3, u2} α R _inst_5 (AddCommMonoid.toAddMonoid.{u2} R _inst_4) _inst_6))))) r A)) (HSMul.hSMul.{u3, u2, u2} α R R (instHSMul.{u3, u2} α R (SMulZeroClass.toSMul.{u3, u2} α R (AddMonoid.toZero.{u2} R (AddCommMonoid.toAddMonoid.{u2} R _inst_4)) (DistribSMul.toSMulZeroClass.{u3, u2} α R (AddMonoid.toAddZeroClass.{u2} R (AddCommMonoid.toAddMonoid.{u2} R _inst_4)) (DistribMulAction.toDistribSMul.{u3, u2} α R _inst_5 (AddCommMonoid.toAddMonoid.{u2} R _inst_4) _inst_6)))) r (Matrix.trace.{u1, u2} n R _inst_2 _inst_4 A))
+Case conversion may be inaccurate. Consider using '#align matrix.trace_smul Matrix.trace_smulₓ'. -/
 @[simp]
 theorem trace_smul [Monoid α] [DistribMulAction α R] (r : α) (A : Matrix n n R) :
     trace (r • A) = r • trace A :=
   Finset.smul_sum.symm
 #align matrix.trace_smul Matrix.trace_smul
 
+/- warning: matrix.trace_transpose -> Matrix.trace_transpose is a dubious translation:
+lean 3 declaration is
+  forall {n : Type.{u1}} {R : Type.{u2}} [_inst_2 : Fintype.{u1} n] [_inst_4 : AddCommMonoid.{u2} R] (A : Matrix.{u1, u1, u2} n n R), Eq.{succ u2} R (Matrix.trace.{u1, u2} n R _inst_2 _inst_4 (Matrix.transpose.{u2, u1, u1} n n R A)) (Matrix.trace.{u1, u2} n R _inst_2 _inst_4 A)
+but is expected to have type
+  forall {n : Type.{u2}} {R : Type.{u1}} [_inst_2 : Fintype.{u2} n] [_inst_4 : AddCommMonoid.{u1} R] (A : Matrix.{u2, u2, u1} n n R), Eq.{succ u1} R (Matrix.trace.{u2, u1} n R _inst_2 _inst_4 (Matrix.transpose.{u1, u2, u2} n n R A)) (Matrix.trace.{u2, u1} n R _inst_2 _inst_4 A)
+Case conversion may be inaccurate. Consider using '#align matrix.trace_transpose Matrix.trace_transposeₓ'. -/
 @[simp]
 theorem trace_transpose (A : Matrix n n R) : trace Aᵀ = trace A :=
   rfl
 #align matrix.trace_transpose Matrix.trace_transpose
 
+#print Matrix.trace_conjTranspose /-
 @[simp]
 theorem trace_conjTranspose [StarAddMonoid R] (A : Matrix n n R) : trace Aᴴ = star (trace A) :=
   (star_sum _ _).symm
 #align matrix.trace_conj_transpose Matrix.trace_conjTranspose
+-/
 
 variable (n α R)
 
+#print Matrix.traceAddMonoidHom /-
 /-- `matrix.trace` as an `add_monoid_hom` -/
 @[simps]
 def traceAddMonoidHom : Matrix n n R →+ R
@@ -85,7 +114,9 @@ def traceAddMonoidHom : Matrix n n R →+ R
   map_zero' := trace_zero n R
   map_add' := trace_add
 #align matrix.trace_add_monoid_hom Matrix.traceAddMonoidHom
+-/
 
+#print Matrix.traceLinearMap /-
 /-- `matrix.trace` as a `linear_map` -/
 @[simps]
 def traceLinearMap [Semiring α] [Module α R] : Matrix n n R →ₗ[α] R
@@ -94,19 +125,34 @@ def traceLinearMap [Semiring α] [Module α R] : Matrix n n R →ₗ[α] R
   map_add' := trace_add
   map_smul' := trace_smul
 #align matrix.trace_linear_map Matrix.traceLinearMap
+-/
 
 variable {n α R}
 
+/- warning: matrix.trace_list_sum -> Matrix.trace_list_sum is a dubious translation:
+lean 3 declaration is
+  forall {n : Type.{u1}} {R : Type.{u2}} [_inst_2 : Fintype.{u1} n] [_inst_4 : AddCommMonoid.{u2} R] (l : List.{max u1 u2} (Matrix.{u1, u1, u2} n n R)), Eq.{succ u2} R (Matrix.trace.{u1, u2} n R _inst_2 _inst_4 (List.sum.{max u1 u2} (Matrix.{u1, u1, u2} n n R) (Matrix.hasAdd.{u2, u1, u1} n n R (AddZeroClass.toHasAdd.{u2} R (AddMonoid.toAddZeroClass.{u2} R (AddCommMonoid.toAddMonoid.{u2} R _inst_4)))) (Matrix.hasZero.{u2, u1, u1} n n R (AddZeroClass.toHasZero.{u2} R (AddMonoid.toAddZeroClass.{u2} R (AddCommMonoid.toAddMonoid.{u2} R _inst_4)))) l)) (List.sum.{u2} R (AddZeroClass.toHasAdd.{u2} R (AddMonoid.toAddZeroClass.{u2} R (AddCommMonoid.toAddMonoid.{u2} R _inst_4))) (AddZeroClass.toHasZero.{u2} R (AddMonoid.toAddZeroClass.{u2} R (AddCommMonoid.toAddMonoid.{u2} R _inst_4))) (List.map.{max u1 u2, u2} (Matrix.{u1, u1, u2} n n R) R (Matrix.trace.{u1, u2} n R _inst_2 _inst_4) l))
+but is expected to have type
+  forall {n : Type.{u1}} {R : Type.{u2}} [_inst_2 : Fintype.{u1} n] [_inst_4 : AddCommMonoid.{u2} R] (l : List.{max u2 u1} (Matrix.{u1, u1, u2} n n R)), Eq.{succ u2} R (Matrix.trace.{u1, u2} n R _inst_2 _inst_4 (List.sum.{max u1 u2} (Matrix.{u1, u1, u2} n n R) (Matrix.add.{u2, u1, u1} n n R (AddZeroClass.toAdd.{u2} R (AddMonoid.toAddZeroClass.{u2} R (AddCommMonoid.toAddMonoid.{u2} R _inst_4)))) (Matrix.zero.{u2, u1, u1} n n R (AddMonoid.toZero.{u2} R (AddCommMonoid.toAddMonoid.{u2} R _inst_4))) l)) (List.sum.{u2} R (AddZeroClass.toAdd.{u2} R (AddMonoid.toAddZeroClass.{u2} R (AddCommMonoid.toAddMonoid.{u2} R _inst_4))) (AddMonoid.toZero.{u2} R (AddCommMonoid.toAddMonoid.{u2} R _inst_4)) (List.map.{max u2 u1, u2} (Matrix.{u1, u1, u2} n n R) R (Matrix.trace.{u1, u2} n R _inst_2 _inst_4) l))
+Case conversion may be inaccurate. Consider using '#align matrix.trace_list_sum Matrix.trace_list_sumₓ'. -/
 @[simp]
 theorem trace_list_sum (l : List (Matrix n n R)) : trace l.Sum = (l.map trace).Sum :=
   map_list_sum (traceAddMonoidHom n R) l
 #align matrix.trace_list_sum Matrix.trace_list_sum
 
+#print Matrix.trace_multiset_sum /-
 @[simp]
 theorem trace_multiset_sum (s : Multiset (Matrix n n R)) : trace s.Sum = (s.map trace).Sum :=
   map_multiset_sum (traceAddMonoidHom n R) s
 #align matrix.trace_multiset_sum Matrix.trace_multiset_sum
+-/
 
+/- warning: matrix.trace_sum -> Matrix.trace_sum is a dubious translation:
+lean 3 declaration is
+  forall {ι : Type.{u1}} {n : Type.{u2}} {R : Type.{u3}} [_inst_2 : Fintype.{u2} n] [_inst_4 : AddCommMonoid.{u3} R] (s : Finset.{u1} ι) (f : ι -> (Matrix.{u2, u2, u3} n n R)), Eq.{succ u3} R (Matrix.trace.{u2, u3} n R _inst_2 _inst_4 (Finset.sum.{max u2 u3, u1} (Matrix.{u2, u2, u3} n n R) ι (Matrix.addCommMonoid.{u3, u2, u2} n n R _inst_4) s (fun (i : ι) => f i))) (Finset.sum.{u3, u1} R ι _inst_4 s (fun (i : ι) => Matrix.trace.{u2, u3} n R _inst_2 _inst_4 (f i)))
+but is expected to have type
+  forall {ι : Type.{u3}} {n : Type.{u2}} {R : Type.{u1}} [_inst_2 : Fintype.{u2} n] [_inst_4 : AddCommMonoid.{u1} R] (s : Finset.{u3} ι) (f : ι -> (Matrix.{u2, u2, u1} n n R)), Eq.{succ u1} R (Matrix.trace.{u2, u1} n R _inst_2 _inst_4 (Finset.sum.{max u1 u2, u3} (Matrix.{u2, u2, u1} n n R) ι (Matrix.addCommMonoid.{u1, u2, u2} n n R _inst_4) s (fun (i : ι) => f i))) (Finset.sum.{u1, u3} R ι _inst_4 s (fun (i : ι) => Matrix.trace.{u2, u1} n R _inst_2 _inst_4 (f i)))
+Case conversion may be inaccurate. Consider using '#align matrix.trace_sum Matrix.trace_sumₓ'. -/
 @[simp]
 theorem trace_sum (s : Finset ι) (f : ι → Matrix n n R) :
     trace (∑ i in s, f i) = ∑ i in s, trace (f i) :=
@@ -119,11 +165,23 @@ section AddCommGroup
 
 variable [AddCommGroup R]
 
+/- warning: matrix.trace_sub -> Matrix.trace_sub is a dubious translation:
+lean 3 declaration is
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+but is expected to have type
+  forall {n : Type.{u2}} {R : Type.{u1}} [_inst_2 : Fintype.{u2} n] [_inst_4 : AddCommGroup.{u1} R] (A : Matrix.{u2, u2, u1} n n R) (B : Matrix.{u2, u2, u1} n n R), Eq.{succ u1} R (Matrix.trace.{u2, u1} n R _inst_2 (AddCommGroup.toAddCommMonoid.{u1} R _inst_4) (HSub.hSub.{max u2 u1, max u2 u1, max u2 u1} (Matrix.{u2, u2, u1} n n R) (Matrix.{u2, u2, u1} n n R) (Matrix.{u2, u2, u1} n n R) (instHSub.{max u2 u1} (Matrix.{u2, u2, u1} n n R) (Matrix.sub.{u1, u2, u2} n n R (SubNegMonoid.toSub.{u1} R (AddGroup.toSubNegMonoid.{u1} R (AddCommGroup.toAddGroup.{u1} R _inst_4))))) A B)) (HSub.hSub.{u1, u1, u1} R R R (instHSub.{u1} R (SubNegMonoid.toSub.{u1} R (AddGroup.toSubNegMonoid.{u1} R (AddCommGroup.toAddGroup.{u1} R _inst_4)))) (Matrix.trace.{u2, u1} n R _inst_2 (AddCommGroup.toAddCommMonoid.{u1} R _inst_4) A) (Matrix.trace.{u2, u1} n R _inst_2 (AddCommGroup.toAddCommMonoid.{u1} R _inst_4) B))
+Case conversion may be inaccurate. Consider using '#align matrix.trace_sub Matrix.trace_subₓ'. -/
 @[simp]
 theorem trace_sub (A B : Matrix n n R) : trace (A - B) = trace A - trace B :=
   Finset.sum_sub_distrib
 #align matrix.trace_sub Matrix.trace_sub
 
+/- warning: matrix.trace_neg -> Matrix.trace_neg is a dubious translation:
+lean 3 declaration is
+  forall {n : Type.{u1}} {R : Type.{u2}} [_inst_2 : Fintype.{u1} n] [_inst_4 : AddCommGroup.{u2} R] (A : Matrix.{u1, u1, u2} n n R), Eq.{succ u2} R (Matrix.trace.{u1, u2} n R _inst_2 (AddCommGroup.toAddCommMonoid.{u2} R _inst_4) (Neg.neg.{max u1 u2} (Matrix.{u1, u1, u2} n n R) (Matrix.hasNeg.{u2, u1, u1} n n R (SubNegMonoid.toHasNeg.{u2} R (AddGroup.toSubNegMonoid.{u2} R (AddCommGroup.toAddGroup.{u2} R _inst_4)))) A)) (Neg.neg.{u2} R (SubNegMonoid.toHasNeg.{u2} R (AddGroup.toSubNegMonoid.{u2} R (AddCommGroup.toAddGroup.{u2} R _inst_4))) (Matrix.trace.{u1, u2} n R _inst_2 (AddCommGroup.toAddCommMonoid.{u2} R _inst_4) A))
+but is expected to have type
+  forall {n : Type.{u2}} {R : Type.{u1}} [_inst_2 : Fintype.{u2} n] [_inst_4 : AddCommGroup.{u1} R] (A : Matrix.{u2, u2, u1} n n R), Eq.{succ u1} R (Matrix.trace.{u2, u1} n R _inst_2 (AddCommGroup.toAddCommMonoid.{u1} R _inst_4) (Neg.neg.{max u2 u1} (Matrix.{u2, u2, u1} n n R) (Matrix.neg.{u1, u2, u2} n n R (NegZeroClass.toNeg.{u1} R (SubNegZeroMonoid.toNegZeroClass.{u1} R (SubtractionMonoid.toSubNegZeroMonoid.{u1} R (SubtractionCommMonoid.toSubtractionMonoid.{u1} R (AddCommGroup.toDivisionAddCommMonoid.{u1} R _inst_4)))))) A)) (Neg.neg.{u1} R (NegZeroClass.toNeg.{u1} R (SubNegZeroMonoid.toNegZeroClass.{u1} R (SubtractionMonoid.toSubNegZeroMonoid.{u1} R (SubtractionCommMonoid.toSubtractionMonoid.{u1} R (AddCommGroup.toDivisionAddCommMonoid.{u1} R _inst_4))))) (Matrix.trace.{u2, u1} n R _inst_2 (AddCommGroup.toAddCommMonoid.{u1} R _inst_4) A))
+Case conversion may be inaccurate. Consider using '#align matrix.trace_neg Matrix.trace_negₓ'. -/
 @[simp]
 theorem trace_neg (A : Matrix n n R) : trace (-A) = -trace A :=
   Finset.sum_neg_distrib
@@ -135,6 +193,12 @@ section One
 
 variable [DecidableEq n] [AddCommMonoidWithOne R]
 
+/- warning: matrix.trace_one -> Matrix.trace_one is a dubious translation:
+lean 3 declaration is
+  forall {n : Type.{u1}} {R : Type.{u2}} [_inst_2 : Fintype.{u1} n] [_inst_4 : DecidableEq.{succ u1} n] [_inst_5 : AddCommMonoidWithOne.{u2} R], Eq.{succ u2} R (Matrix.trace.{u1, u2} n R _inst_2 (AddCommMonoidWithOne.toAddCommMonoid.{u2} R _inst_5) (OfNat.ofNat.{max u1 u2} (Matrix.{u1, u1, u2} n n R) 1 (OfNat.mk.{max u1 u2} (Matrix.{u1, u1, u2} n n R) 1 (One.one.{max u1 u2} (Matrix.{u1, u1, u2} n n R) (Matrix.hasOne.{u2, u1} n R (fun (a : n) (b : n) => _inst_4 a b) (AddZeroClass.toHasZero.{u2} R (AddMonoid.toAddZeroClass.{u2} R (AddMonoidWithOne.toAddMonoid.{u2} R (AddCommMonoidWithOne.toAddMonoidWithOne.{u2} R _inst_5)))) (AddMonoidWithOne.toOne.{u2} R (AddCommMonoidWithOne.toAddMonoidWithOne.{u2} R _inst_5))))))) ((fun (a : Type) (b : Type.{u2}) [self : HasLiftT.{1, succ u2} a b] => self.0) Nat R (HasLiftT.mk.{1, succ u2} Nat R (CoeTCₓ.coe.{1, succ u2} Nat R (Nat.castCoe.{u2} R (AddMonoidWithOne.toNatCast.{u2} R (AddCommMonoidWithOne.toAddMonoidWithOne.{u2} R _inst_5))))) (Fintype.card.{u1} n _inst_2))
+but is expected to have type
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+Case conversion may be inaccurate. Consider using '#align matrix.trace_one Matrix.trace_oneₓ'. -/
 @[simp]
 theorem trace_one : trace (1 : Matrix n n R) = Fintype.card n := by
   simp_rw [trace, diag_one, Pi.one_def, Finset.sum_const, nsmul_one, Finset.card_univ]
@@ -144,26 +208,56 @@ end One
 
 section Mul
 
+/- warning: matrix.trace_transpose_mul -> Matrix.trace_transpose_mul is a dubious translation:
+lean 3 declaration is
+  forall {m : Type.{u1}} {n : Type.{u2}} {R : Type.{u3}} [_inst_1 : Fintype.{u1} m] [_inst_2 : Fintype.{u2} n] [_inst_4 : AddCommMonoid.{u3} R] [_inst_5 : Mul.{u3} R] (A : Matrix.{u1, u2, u3} m n R) (B : Matrix.{u2, u1, u3} n m R), Eq.{succ u3} R (Matrix.trace.{u2, u3} n R _inst_2 _inst_4 (Matrix.mul.{u3, u2, u1, u2} n m n R _inst_1 _inst_5 _inst_4 (Matrix.transpose.{u3, u1, u2} m n R A) (Matrix.transpose.{u3, u2, u1} n m R B))) (Matrix.trace.{u1, u3} m R _inst_1 _inst_4 (Matrix.mul.{u3, u1, u2, u1} m n m R _inst_2 _inst_5 _inst_4 A B))
+but is expected to have type
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+Case conversion may be inaccurate. Consider using '#align matrix.trace_transpose_mul Matrix.trace_transpose_mulₓ'. -/
 @[simp]
 theorem trace_transpose_mul [AddCommMonoid R] [Mul R] (A : Matrix m n R) (B : Matrix n m R) :
     trace (Aᵀ ⬝ Bᵀ) = trace (A ⬝ B) :=
   Finset.sum_comm
 #align matrix.trace_transpose_mul Matrix.trace_transpose_mul
 
+/- warning: matrix.trace_mul_comm -> Matrix.trace_mul_comm is a dubious translation:
+lean 3 declaration is
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+Case conversion may be inaccurate. Consider using '#align matrix.trace_mul_comm Matrix.trace_mul_commₓ'. -/
 theorem trace_mul_comm [AddCommMonoid R] [CommSemigroup R] (A : Matrix m n R) (B : Matrix n m R) :
     trace (A ⬝ B) = trace (B ⬝ A) := by rw [← trace_transpose, ← trace_transpose_mul, transpose_mul]
 #align matrix.trace_mul_comm Matrix.trace_mul_comm
 
+/- warning: matrix.trace_mul_cycle -> Matrix.trace_mul_cycle is a dubious translation:
+lean 3 declaration is
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+Case conversion may be inaccurate. Consider using '#align matrix.trace_mul_cycle Matrix.trace_mul_cycleₓ'. -/
 theorem trace_mul_cycle [NonUnitalCommSemiring R] (A : Matrix m n R) (B : Matrix n p R)
     (C : Matrix p m R) : trace (A ⬝ B ⬝ C) = trace (C ⬝ A ⬝ B) := by
   rw [trace_mul_comm, Matrix.mul_assoc]
 #align matrix.trace_mul_cycle Matrix.trace_mul_cycle
 
+/- warning: matrix.trace_mul_cycle' -> Matrix.trace_mul_cycle' is a dubious translation:
+lean 3 declaration is
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+Case conversion may be inaccurate. Consider using '#align matrix.trace_mul_cycle' Matrix.trace_mul_cycle'ₓ'. -/
 theorem trace_mul_cycle' [NonUnitalCommSemiring R] (A : Matrix m n R) (B : Matrix n p R)
     (C : Matrix p m R) : trace (A ⬝ (B ⬝ C)) = trace (C ⬝ (A ⬝ B)) := by
   rw [← Matrix.mul_assoc, trace_mul_comm]
 #align matrix.trace_mul_cycle' Matrix.trace_mul_cycle'
 
+/- warning: matrix.trace_col_mul_row -> Matrix.trace_col_mul_row is a dubious translation:
+lean 3 declaration is
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+but is expected to have type
+  forall {n : Type.{u1}} {R : Type.{u2}} [_inst_2 : Fintype.{u1} n] [_inst_4 : NonUnitalNonAssocSemiring.{u2} R] (a : n -> R) (b : n -> R), Eq.{succ u2} R (Matrix.trace.{u1, u2} n R _inst_2 (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} R _inst_4) (Matrix.mul.{u2, u1, 0, u1} n Unit n R PUnit.fintype.{0} (NonUnitalNonAssocSemiring.toMul.{u2} R _inst_4) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} R _inst_4) (Matrix.col.{u2, u1} n R a) (Matrix.row.{u2, u1} n R b))) (Matrix.dotProduct.{u2, u1} n R _inst_2 (NonUnitalNonAssocSemiring.toMul.{u2} R _inst_4) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} R _inst_4) a b)
+Case conversion may be inaccurate. Consider using '#align matrix.trace_col_mul_row Matrix.trace_col_mul_rowₓ'. -/
 @[simp]
 theorem trace_col_mul_row [NonUnitalNonAssocSemiring R] (a b : n → R) :
     trace (col a ⬝ row b) = dotProduct a b := by simp [dot_product, trace]
@@ -182,19 +276,43 @@ with `matrix.det_fin_two` etc.
 -/
 
 
+/- warning: matrix.trace_fin_zero -> Matrix.trace_fin_zero is a dubious translation:
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+but is expected to have type
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+Case conversion may be inaccurate. Consider using '#align matrix.trace_fin_zero Matrix.trace_fin_zeroₓ'. -/
 @[simp]
 theorem trace_fin_zero (A : Matrix (Fin 0) (Fin 0) R) : trace A = 0 :=
   rfl
 #align matrix.trace_fin_zero Matrix.trace_fin_zero
 
+/- warning: matrix.trace_fin_one -> Matrix.trace_fin_one is a dubious translation:
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+Case conversion may be inaccurate. Consider using '#align matrix.trace_fin_one Matrix.trace_fin_oneₓ'. -/
 theorem trace_fin_one (A : Matrix (Fin 1) (Fin 1) R) : trace A = A 0 0 :=
   add_zero _
 #align matrix.trace_fin_one Matrix.trace_fin_one
 
+/- warning: matrix.trace_fin_two -> Matrix.trace_fin_two is a dubious translation:
+lean 3 declaration is
+  forall {R : Type.{u1}} [_inst_4 : AddCommMonoid.{u1} R] (A : Matrix.{0, 0, u1} (Fin (OfNat.ofNat.{0} Nat 2 (OfNat.mk.{0} Nat 2 (bit0.{0} Nat Nat.hasAdd (One.one.{0} Nat Nat.hasOne))))) (Fin (OfNat.ofNat.{0} Nat 2 (OfNat.mk.{0} Nat 2 (bit0.{0} Nat Nat.hasAdd (One.one.{0} Nat Nat.hasOne))))) R), Eq.{succ u1} R (Matrix.trace.{0, u1} (Fin (OfNat.ofNat.{0} Nat 2 (OfNat.mk.{0} Nat 2 (bit0.{0} Nat Nat.hasAdd (One.one.{0} Nat Nat.hasOne))))) R (Fin.fintype (OfNat.ofNat.{0} Nat 2 (OfNat.mk.{0} Nat 2 (bit0.{0} Nat Nat.hasAdd (One.one.{0} Nat Nat.hasOne))))) _inst_4 A) (HAdd.hAdd.{u1, u1, u1} R R R (instHAdd.{u1} R (AddZeroClass.toHasAdd.{u1} R (AddMonoid.toAddZeroClass.{u1} R (AddCommMonoid.toAddMonoid.{u1} R _inst_4)))) (A (OfNat.ofNat.{0} (Fin (bit0.{0} Nat Nat.hasAdd (One.one.{0} Nat Nat.hasOne))) 0 (OfNat.mk.{0} (Fin (bit0.{0} Nat Nat.hasAdd (One.one.{0} Nat Nat.hasOne))) 0 (Zero.zero.{0} (Fin (bit0.{0} Nat Nat.hasAdd (One.one.{0} Nat Nat.hasOne))) (Fin.hasZeroOfNeZero (bit0.{0} Nat Nat.hasAdd (One.one.{0} Nat Nat.hasOne)) (CharZero.NeZero.two.{0} Nat (AddCommMonoidWithOne.toAddMonoidWithOne.{0} Nat (NonAssocSemiring.toAddCommMonoidWithOne.{0} Nat (Semiring.toNonAssocSemiring.{0} Nat Nat.semiring))) (StrictOrderedSemiring.to_charZero.{0} Nat Nat.strictOrderedSemiring)))))) (OfNat.ofNat.{0} (Fin (bit0.{0} Nat Nat.hasAdd (One.one.{0} Nat Nat.hasOne))) 0 (OfNat.mk.{0} (Fin (bit0.{0} Nat Nat.hasAdd (One.one.{0} Nat Nat.hasOne))) 0 (Zero.zero.{0} (Fin (bit0.{0} Nat Nat.hasAdd (One.one.{0} Nat Nat.hasOne))) (Fin.hasZeroOfNeZero (bit0.{0} Nat Nat.hasAdd (One.one.{0} Nat Nat.hasOne)) (CharZero.NeZero.two.{0} Nat (AddCommMonoidWithOne.toAddMonoidWithOne.{0} Nat (NonAssocSemiring.toAddCommMonoidWithOne.{0} Nat (Semiring.toNonAssocSemiring.{0} Nat Nat.semiring))) (StrictOrderedSemiring.to_charZero.{0} Nat Nat.strictOrderedSemiring))))))) (A (OfNat.ofNat.{0} (Fin (bit0.{0} Nat Nat.hasAdd (One.one.{0} Nat Nat.hasOne))) 1 (OfNat.mk.{0} (Fin (bit0.{0} Nat Nat.hasAdd (One.one.{0} Nat Nat.hasOne))) 1 (One.one.{0} (Fin (bit0.{0} Nat Nat.hasAdd (One.one.{0} Nat Nat.hasOne))) (Fin.hasOneOfNeZero (bit0.{0} Nat Nat.hasAdd (One.one.{0} Nat Nat.hasOne)) (CharZero.NeZero.two.{0} Nat (AddCommMonoidWithOne.toAddMonoidWithOne.{0} Nat (NonAssocSemiring.toAddCommMonoidWithOne.{0} Nat (Semiring.toNonAssocSemiring.{0} Nat Nat.semiring))) (StrictOrderedSemiring.to_charZero.{0} Nat Nat.strictOrderedSemiring)))))) (OfNat.ofNat.{0} (Fin (bit0.{0} Nat Nat.hasAdd (One.one.{0} Nat Nat.hasOne))) 1 (OfNat.mk.{0} (Fin (bit0.{0} Nat Nat.hasAdd (One.one.{0} Nat Nat.hasOne))) 1 (One.one.{0} (Fin (bit0.{0} Nat Nat.hasAdd (One.one.{0} Nat Nat.hasOne))) (Fin.hasOneOfNeZero (bit0.{0} Nat Nat.hasAdd (One.one.{0} Nat Nat.hasOne)) (CharZero.NeZero.two.{0} Nat (AddCommMonoidWithOne.toAddMonoidWithOne.{0} Nat (NonAssocSemiring.toAddCommMonoidWithOne.{0} Nat (Semiring.toNonAssocSemiring.{0} Nat Nat.semiring))) (StrictOrderedSemiring.to_charZero.{0} Nat Nat.strictOrderedSemiring))))))))
+but is expected to have type
+  forall {R : Type.{u1}} [_inst_4 : AddCommMonoid.{u1} R] (A : Matrix.{0, 0, u1} (Fin (OfNat.ofNat.{0} Nat 2 (instOfNatNat 2))) (Fin (OfNat.ofNat.{0} Nat 2 (instOfNatNat 2))) R), Eq.{succ u1} R (Matrix.trace.{0, u1} (Fin (OfNat.ofNat.{0} Nat 2 (instOfNatNat 2))) R (Fin.fintype (OfNat.ofNat.{0} Nat 2 (instOfNatNat 2))) _inst_4 A) (HAdd.hAdd.{u1, u1, u1} R R R (instHAdd.{u1} R (AddZeroClass.toAdd.{u1} R (AddMonoid.toAddZeroClass.{u1} R (AddCommMonoid.toAddMonoid.{u1} R _inst_4)))) (A (OfNat.ofNat.{0} (Fin (OfNat.ofNat.{0} Nat 2 (instOfNatNat 2))) 0 (Fin.instOfNatFin (OfNat.ofNat.{0} Nat 2 (instOfNatNat 2)) 0 (NeZero.succ (OfNat.ofNat.{0} Nat 1 (instOfNatNat 1))))) (OfNat.ofNat.{0} (Fin (OfNat.ofNat.{0} Nat 2 (instOfNatNat 2))) 0 (Fin.instOfNatFin (OfNat.ofNat.{0} Nat 2 (instOfNatNat 2)) 0 (NeZero.succ (OfNat.ofNat.{0} Nat 1 (instOfNatNat 1)))))) (A (OfNat.ofNat.{0} (Fin (OfNat.ofNat.{0} Nat 2 (instOfNatNat 2))) 1 (Fin.instOfNatFin (OfNat.ofNat.{0} Nat 2 (instOfNatNat 2)) 1 (NeZero.succ (OfNat.ofNat.{0} Nat 1 (instOfNatNat 1))))) (OfNat.ofNat.{0} (Fin (OfNat.ofNat.{0} Nat 2 (instOfNatNat 2))) 1 (Fin.instOfNatFin (OfNat.ofNat.{0} Nat 2 (instOfNatNat 2)) 1 (NeZero.succ (OfNat.ofNat.{0} Nat 1 (instOfNatNat 1)))))))
+Case conversion may be inaccurate. Consider using '#align matrix.trace_fin_two Matrix.trace_fin_twoₓ'. -/
 theorem trace_fin_two (A : Matrix (Fin 2) (Fin 2) R) : trace A = A 0 0 + A 1 1 :=
   congr_arg ((· + ·) _) (add_zero (A 1 1))
 #align matrix.trace_fin_two Matrix.trace_fin_two
 
+/- warning: matrix.trace_fin_three -> Matrix.trace_fin_three is a dubious translation:
+lean 3 declaration is
+  forall {R : Type.{u1}} [_inst_4 : AddCommMonoid.{u1} R] (A : Matrix.{0, 0, u1} (Fin (OfNat.ofNat.{0} Nat 3 (OfNat.mk.{0} Nat 3 (bit1.{0} Nat Nat.hasOne Nat.hasAdd (One.one.{0} Nat Nat.hasOne))))) (Fin (OfNat.ofNat.{0} Nat 3 (OfNat.mk.{0} Nat 3 (bit1.{0} Nat Nat.hasOne Nat.hasAdd (One.one.{0} Nat Nat.hasOne))))) R), Eq.{succ u1} R (Matrix.trace.{0, u1} (Fin (OfNat.ofNat.{0} Nat 3 (OfNat.mk.{0} Nat 3 (bit1.{0} Nat Nat.hasOne Nat.hasAdd (One.one.{0} Nat Nat.hasOne))))) R (Fin.fintype (OfNat.ofNat.{0} Nat 3 (OfNat.mk.{0} Nat 3 (bit1.{0} Nat Nat.hasOne Nat.hasAdd (One.one.{0} Nat Nat.hasOne))))) _inst_4 A) (HAdd.hAdd.{u1, u1, u1} R R R (instHAdd.{u1} R (AddZeroClass.toHasAdd.{u1} R (AddMonoid.toAddZeroClass.{u1} R (AddCommMonoid.toAddMonoid.{u1} R _inst_4)))) (HAdd.hAdd.{u1, u1, u1} R R R (instHAdd.{u1} R (AddZeroClass.toHasAdd.{u1} R (AddMonoid.toAddZeroClass.{u1} R (AddCommMonoid.toAddMonoid.{u1} R _inst_4)))) (A (OfNat.ofNat.{0} (Fin (bit1.{0} Nat Nat.hasOne Nat.hasAdd (One.one.{0} 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(OrderedAddCommMonoid.to_covariantClass_left.{0} Nat (OrderedSemiring.toOrderedAddCommMonoid.{0} Nat Nat.orderedSemiring)))))))) (OfNat.ofNat.{0} (Fin (bit1.{0} Nat Nat.hasOne Nat.hasAdd (One.one.{0} Nat Nat.hasOne))) 2 (OfNat.mk.{0} (Fin (bit1.{0} Nat Nat.hasOne Nat.hasAdd (One.one.{0} Nat Nat.hasOne))) 2 (bit0.{0} (Fin (bit1.{0} Nat Nat.hasOne Nat.hasAdd (One.one.{0} Nat Nat.hasOne))) (Fin.hasAdd (bit1.{0} Nat Nat.hasOne Nat.hasAdd (One.one.{0} Nat Nat.hasOne))) (One.one.{0} (Fin (bit1.{0} Nat Nat.hasOne Nat.hasAdd (One.one.{0} Nat Nat.hasOne))) (Fin.hasOneOfNeZero (bit1.{0} Nat Nat.hasOne Nat.hasAdd (One.one.{0} Nat Nat.hasOne)) (ZeroLEOneClass.NeZero.three.{0} Nat (AddCommMonoidWithOne.toAddMonoidWithOne.{0} Nat (NonAssocSemiring.toAddCommMonoidWithOne.{0} Nat (Semiring.toNonAssocSemiring.{0} Nat Nat.semiring))) (OrderedCancelAddCommMonoid.toPartialOrder.{0} Nat (StrictOrderedSemiring.toOrderedCancelAddCommMonoid.{0} Nat Nat.strictOrderedSemiring)) (OrderedSemiring.zeroLEOneClass.{0} Nat Nat.orderedSemiring) (NeZero.one.{0} Nat (NonAssocSemiring.toMulZeroOneClass.{0} Nat (Semiring.toNonAssocSemiring.{0} Nat Nat.semiring)) Nat.nontrivial) (OrderedAddCommMonoid.to_covariantClass_left.{0} Nat (OrderedSemiring.toOrderedAddCommMonoid.{0} Nat Nat.orderedSemiring))))))))))
+but is expected to have type
+  forall {R : Type.{u1}} [_inst_4 : AddCommMonoid.{u1} R] (A : Matrix.{0, 0, u1} (Fin (OfNat.ofNat.{0} Nat 3 (instOfNatNat 3))) (Fin (OfNat.ofNat.{0} Nat 3 (instOfNatNat 3))) R), Eq.{succ u1} R (Matrix.trace.{0, u1} (Fin (OfNat.ofNat.{0} Nat 3 (instOfNatNat 3))) R (Fin.fintype (OfNat.ofNat.{0} Nat 3 (instOfNatNat 3))) _inst_4 A) (HAdd.hAdd.{u1, u1, u1} R R R (instHAdd.{u1} R (AddZeroClass.toAdd.{u1} R (AddMonoid.toAddZeroClass.{u1} R (AddCommMonoid.toAddMonoid.{u1} R _inst_4)))) (HAdd.hAdd.{u1, u1, u1} R R R (instHAdd.{u1} R (AddZeroClass.toAdd.{u1} R (AddMonoid.toAddZeroClass.{u1} R (AddCommMonoid.toAddMonoid.{u1} R _inst_4)))) (A (OfNat.ofNat.{0} (Fin (OfNat.ofNat.{0} Nat 3 (instOfNatNat 3))) 0 (Fin.instOfNatFin (OfNat.ofNat.{0} Nat 3 (instOfNatNat 3)) 0 (NeZero.succ (OfNat.ofNat.{0} Nat 2 (instOfNatNat 2))))) (OfNat.ofNat.{0} (Fin (OfNat.ofNat.{0} Nat 3 (instOfNatNat 3))) 0 (Fin.instOfNatFin (OfNat.ofNat.{0} Nat 3 (instOfNatNat 3)) 0 (NeZero.succ (OfNat.ofNat.{0} Nat 2 (instOfNatNat 2)))))) (A (OfNat.ofNat.{0} (Fin (OfNat.ofNat.{0} Nat 3 (instOfNatNat 3))) 1 (Fin.instOfNatFin (OfNat.ofNat.{0} Nat 3 (instOfNatNat 3)) 1 (NeZero.succ (OfNat.ofNat.{0} Nat 2 (instOfNatNat 2))))) (OfNat.ofNat.{0} (Fin (OfNat.ofNat.{0} Nat 3 (instOfNatNat 3))) 1 (Fin.instOfNatFin (OfNat.ofNat.{0} Nat 3 (instOfNatNat 3)) 1 (NeZero.succ (OfNat.ofNat.{0} Nat 2 (instOfNatNat 2))))))) (A (OfNat.ofNat.{0} (Fin (OfNat.ofNat.{0} Nat 3 (instOfNatNat 3))) 2 (Fin.instOfNatFin (OfNat.ofNat.{0} Nat 3 (instOfNatNat 3)) 2 (NeZero.succ (OfNat.ofNat.{0} Nat 2 (instOfNatNat 2))))) (OfNat.ofNat.{0} (Fin (OfNat.ofNat.{0} Nat 3 (instOfNatNat 3))) 2 (Fin.instOfNatFin (OfNat.ofNat.{0} Nat 3 (instOfNatNat 3)) 2 (NeZero.succ (OfNat.ofNat.{0} Nat 2 (instOfNatNat 2)))))))
+Case conversion may be inaccurate. Consider using '#align matrix.trace_fin_three Matrix.trace_fin_threeₓ'. -/
 theorem trace_fin_three (A : Matrix (Fin 3) (Fin 3) R) : trace A = A 0 0 + A 1 1 + A 2 2 :=
   by
   rw [← add_zero (A 2 2), add_assoc]

32b08ef8

bump to nightly-2023-02-21-16

mathlib commit https://github.com/leanprover-community/mathlib/commit/bd9851ca476957ea4549eb19b40e7b5ade9428cc

1107b979

Changes in mathlib4

mathlib3

mathlib4

32b08ef8

chore(*): remove empty lines between variable statements (#11418)

Empty lines were removed by executing the following Python script twice

import os
import re


# Loop through each file in the repository
for dir_path, dirs, files in os.walk('.'):
  for filename in files:
    if filename.endswith('.lean'):
      file_path = os.path.join(dir_path, filename)

      # Open the file and read its contents
      with open(file_path, 'r') as file:
        content = file.read()

      # Use a regular expression to replace sequences of "variable" lines separated by empty lines
      # with sequences without empty lines
      modified_content = re.sub(r'(variable.*\n)\n(variable(?! .* in))', r'\1\2', content)

      # Write the modified content back to the file
      with open(file_path, 'w') as file:
        file.write(modified_content)

75c86f04

Diff

@@ -29,7 +29,6 @@ open BigOperators Matrix
 namespace Matrix
 
 variable {ι m n p : Type*} {α R S : Type*}
-
 variable [Fintype m] [Fintype n] [Fintype p]
 
 section AddCommMonoid

32b08ef8

chore: Replace (· op ·) a by (a op ·) (#8843)

I used the regex $\(· (.) ·$ (.)\), replacing with ($2 $1 ·).

d14658b4

Diff

@@ -217,7 +217,7 @@ theorem trace_fin_one (A : Matrix (Fin 1) (Fin 1) R) : trace A = A 0 0 :=
 #align matrix.trace_fin_one Matrix.trace_fin_one
 
 theorem trace_fin_two (A : Matrix (Fin 2) (Fin 2) R) : trace A = A 0 0 + A 1 1 :=
-  congr_arg ((· + ·) _) (add_zero (A 1 1))
+  congr_arg (_ + ·) (add_zero (A 1 1))
 #align matrix.trace_fin_two Matrix.trace_fin_two
 
 theorem trace_fin_three (A : Matrix (Fin 3) (Fin 3) R) : trace A = A 0 0 + A 1 1 + A 2 2 := by

32b08ef8

feat: Add norm_one_add_smul. (#8681)

Co-authored-by: Andrew Yang <36414270+erdOne@users.noreply.github.com>

dc62cf3f

Diff

@@ -190,6 +190,13 @@ theorem trace_col_mul_row [NonUnitalNonAssocSemiring R] (a b : n → R) :
 
 end Mul
 
+lemma trace_submatrix_succ {n : ℕ} [NonUnitalNonAssocSemiring R]
+    (M : Matrix (Fin n.succ) (Fin n.succ) R) :
+    M 0 0 + trace (submatrix M Fin.succ Fin.succ) = trace M := by
+  delta trace
+  rw [← (finSuccEquiv n).symm.sum_comp]
+  simp
+
 section Fin
 
 variable [AddCommMonoid R]

32b08ef8

feat: the trace of a direct sum is the sum of the traces (#8369)

0e1fb8d5

Diff

@@ -4,6 +4,7 @@ Released under Apache 2.0 license as described in the file LICENSE.
 Authors: Johannes Hölzl, Patrick Massot, Casper Putz, Anne Baanen
 -/
 import Mathlib.Data.Matrix.Basic
+import Mathlib.Data.Matrix.Block
 import Mathlib.Data.Matrix.RowCol
 
 #align_import linear_algebra.matrix.trace from "leanprover-community/mathlib"@"32b08ef840dd25ca2e47e035c5da03ce16d2dc3c"
@@ -120,6 +121,15 @@ theorem _root_.AddMonoidHom.map_trace [AddCommMonoid S] (f : R →+ S) (A : Matr
     f (trace A)  = trace (f.mapMatrix A) :=
   map_sum f (fun i => diag A i) Finset.univ
 
+lemma trace_blockDiagonal [DecidableEq p] (M : p → Matrix n n R) :
+    trace (blockDiagonal M) = ∑ i, trace (M i) := by
+  simp [blockDiagonal, trace, Finset.sum_comm (γ := n)]
+
+lemma trace_blockDiagonal' [DecidableEq p] {m : p → Type*} [∀ i, Fintype (m i)]
+    (M : ∀ i, Matrix (m i) (m i) R) :
+    trace (blockDiagonal' M) = ∑ i, trace (M i) := by
+  simp [blockDiagonal', trace, Finset.sum_sigma']
+
 end AddCommMonoid
 
 section AddCommGroup

32b08ef8

refactor(Data/Matrix/Basic): split row/column decls (#8089)

This splits out row/col/updateRow/updateColumn to their own file, as Data/Matrix/Basic is getting rather large.

The copyright comes from https://github.com/leanprover-community/mathlib/pull/1816 and https://github.com/leanprover-community/mathlib/pull/2480

There are no new lemmas in this PR, nor were any existing lemmas deleted.

It's possible that even more lemmas could migrate to this new file (for instance, flipping the import with Matrix.Notation or LinearAlgebra.Matrix.Trace), but I've taken the conservative option of leaving those lemmas alone for now.

ee77c382

Diff

@@ -4,6 +4,7 @@ Released under Apache 2.0 license as described in the file LICENSE.
 Authors: Johannes Hölzl, Patrick Massot, Casper Putz, Anne Baanen
 -/
 import Mathlib.Data.Matrix.Basic
+import Mathlib.Data.Matrix.RowCol
 
 #align_import linear_algebra.matrix.trace from "leanprover-community/mathlib"@"32b08ef840dd25ca2e47e035c5da03ce16d2dc3c"

32b08ef8

feat(LinearAlgebra/Matrix/Trace): add Matrix.trace_diagonal (#7061)

The trace of a diagonal matrix is the sum of the diagonal elements.

Zulip discussion

ab88fbbd

Diff

@@ -42,6 +42,10 @@ def trace (A : Matrix n n R) : R :=
   ∑ i, diag A i
 #align matrix.trace Matrix.trace
 
+lemma trace_diagonal {o} [Fintype o] [DecidableEq o] (d : o → R) :
+    trace (diagonal d) = ∑ i, d i := by
+  simp only [trace, diag_apply, diagonal_apply_eq]
+
 variable (n R)
 
 @[simp]

32b08ef8

feat: nilpotent matrices have nilpotent trace (#6588)

Also some related results

Co-authored-by: damiano <adomani@gmail.com>

351431b2

Diff

@@ -51,6 +51,9 @@ theorem trace_zero : trace (0 : Matrix n n R) = 0 :=
 
 variable {n R}
 
+@[simp]
+lemma trace_eq_zero_of_isEmpty [IsEmpty n] (A : Matrix n n R) : trace A = 0 := by simp [trace]
+
 @[simp]
 theorem trace_add (A B : Matrix n n R) : trace (A + B) = trace A + trace B :=
   Finset.sum_add_distrib
@@ -183,7 +186,6 @@ with `Matrix.det_fin_two` etc.
 -/
 
 
-@[simp]
 theorem trace_fin_zero (A : Matrix (Fin 0) (Fin 0) R) : trace A = 0 :=
   rfl
 #align matrix.trace_fin_zero Matrix.trace_fin_zero

32b08ef8

refactor(Data/Matrix): Eliminate ⬝ notation in favor of HMul (#6487)

The main difficulty here is that * has a slightly difference precedence to ⬝. notably around smul and neg.

The other annoyance is that ↑U ⬝ A ⬝ ↑U⁻¹ : Matrix m m 𝔸 now has to be written U.val * A * (U⁻¹).val in order to typecheck.

A downside of this change to consider: if you have a goal of A * (B * C) = (A * B) * C, mul_assoc now gives the illusion of matching, when in fact Matrix.mul_assoc is needed. Previously the distinct symbol made it easy to avoid this mistake.

On the flipside, there is now no need to rewrite by Matrix.mul_eq_mul all the time (indeed, the lemma is now removed).

38c07226

Diff

@@ -145,27 +145,27 @@ section Mul
 
 @[simp]
 theorem trace_transpose_mul [AddCommMonoid R] [Mul R] (A : Matrix m n R) (B : Matrix n m R) :
-    trace (Aᵀ ⬝ Bᵀ) = trace (A ⬝ B) :=
+    trace (Aᵀ * Bᵀ) = trace (A * B) :=
   Finset.sum_comm
 #align matrix.trace_transpose_mul Matrix.trace_transpose_mul
 
 theorem trace_mul_comm [AddCommMonoid R] [CommSemigroup R] (A : Matrix m n R) (B : Matrix n m R) :
-    trace (A ⬝ B) = trace (B ⬝ A) := by rw [← trace_transpose, ← trace_transpose_mul, transpose_mul]
+    trace (A * B) = trace (B * A) := by rw [← trace_transpose, ← trace_transpose_mul, transpose_mul]
 #align matrix.trace_mul_comm Matrix.trace_mul_comm
 
 theorem trace_mul_cycle [NonUnitalCommSemiring R] (A : Matrix m n R) (B : Matrix n p R)
-    (C : Matrix p m R) : trace (A ⬝ B ⬝ C) = trace (C ⬝ A ⬝ B) := by
+    (C : Matrix p m R) : trace (A * B * C) = trace (C * A * B) := by
   rw [trace_mul_comm, Matrix.mul_assoc]
 #align matrix.trace_mul_cycle Matrix.trace_mul_cycle
 
 theorem trace_mul_cycle' [NonUnitalCommSemiring R] (A : Matrix m n R) (B : Matrix n p R)
-    (C : Matrix p m R) : trace (A ⬝ (B ⬝ C)) = trace (C ⬝ (A ⬝ B)) := by
+    (C : Matrix p m R) : trace (A * (B * C)) = trace (C * (A * B)) := by
   rw [← Matrix.mul_assoc, trace_mul_comm]
 #align matrix.trace_mul_cycle' Matrix.trace_mul_cycle'
 
 @[simp]
 theorem trace_col_mul_row [NonUnitalNonAssocSemiring R] (a b : n → R) :
-    trace (col a ⬝ row b) = dotProduct a b := by
+    trace (col a * row b) = dotProduct a b := by
   apply Finset.sum_congr rfl
   simp [mul_apply]
 #align matrix.trace_col_mul_row Matrix.trace_col_mul_row

32b08ef8

feat: add Algebra.discr_localizationLocalization (#6422)

We prove

theorem Algebra.discr_localizationLocalization (b : Basis ι R S) :
  Algebra.discr Rₘ (b.localizationLocalization Rₘ M Aₘ) = algebraMap R Rₘ (Algebra.discr R b)

We need for that to prove the analogue for the trace of Algebra.norm_localization (that was the only result in RingTheory.Localization.Norm). Since the results are added to this file, it is renamed to RingTheory.Localization.NormTrace (not sure about the name though).

ec529253

Diff

@@ -108,6 +108,10 @@ theorem trace_sum (s : Finset ι) (f : ι → Matrix n n R) :
   map_sum (traceAddMonoidHom n R) f s
 #align matrix.trace_sum Matrix.trace_sum
 
+theorem _root_.AddMonoidHom.map_trace [AddCommMonoid S] (f : R →+ S) (A : Matrix n n R) :
+    f (trace A)  = trace (f.mapMatrix A) :=
+  map_sum f (fun i => diag A i) Finset.univ
+
 end AddCommMonoid
 
 section AddCommGroup

32b08ef8

chore: banish Type _ and Sort _ (#6499)

We remove all possible occurences of Type _ and Sort _ in favor of Type* and Sort*.

This has nice performance benefits.

32de3f67

Diff

@@ -26,7 +26,7 @@ open BigOperators Matrix
 
 namespace Matrix
 
-variable {ι m n p : Type _} {α R S : Type _}
+variable {ι m n p : Type*} {α R S : Type*}
 
 variable [Fintype m] [Fintype n] [Fintype p]

32b08ef8

chore: script to replace headers with #align_import statements (#5979)

depends on: #5966

Co-authored-by: Eric Wieser <wieser.eric@gmail.com> Co-authored-by: Scott Morrison <scott.morrison@gmail.com>

89aa3a3b

Diff

@@ -2,14 +2,11 @@
 Copyright (c) 2019 Johannes Hölzl. All rights reserved.
 Released under Apache 2.0 license as described in the file LICENSE.
 Authors: Johannes Hölzl, Patrick Massot, Casper Putz, Anne Baanen
-
-! This file was ported from Lean 3 source module linear_algebra.matrix.trace
-! leanprover-community/mathlib commit 32b08ef840dd25ca2e47e035c5da03ce16d2dc3c
-! Please do not edit these lines, except to modify the commit id
-! if you have ported upstream changes.
 -/
 import Mathlib.Data.Matrix.Basic
 
+#align_import linear_algebra.matrix.trace from "leanprover-community/mathlib"@"32b08ef840dd25ca2e47e035c5da03ce16d2dc3c"
+
 /-!
 # Trace of a matrix

32b08ef8

feat: port LinearAlgebra.Matrix.Trace (#3231)

Co-authored-by: Parcly Taxel <reddeloostw@gmail.com>

1c65b428

`linear_algebra.matrix.trace` ⟷ `Mathlib.LinearAlgebra.Matrix.Trace`

Changes since the initial port

Changes in mathlib3

Changes in mathlib3port

Changes in mathlib4

Dependencies 8 + 384

linear_algebra.matrix.trace ⟷ Mathlib.LinearAlgebra.Matrix.Trace

Changes since the initial port

Changes in mathlib3

Changes in mathlib3port

Changes in mathlib4

Dependencies 8 + 384

`linear_algebra.matrix.trace` ⟷ `Mathlib.LinearAlgebra.Matrix.Trace`