linear_algebra.matrix.symmetric ⟷ Mathlib.LinearAlgebra.Matrix.Symmetric

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

@@ -3,7 +3,7 @@ Copyright (c) 2021 Lu-Ming Zhang. All rights reserved.
 Released under Apache 2.0 license as described in the file LICENSE.
 Authors: Lu-Ming Zhang
 -/
-import Mathbin.Data.Matrix.Block
+import Data.Matrix.Block
 
 #align_import linear_algebra.matrix.symmetric from "leanprover-community/mathlib"@"d64d67d000b974f0d86a2be7918cf800be6271c8"
 

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

@@ -2,14 +2,11 @@
 Copyright (c) 2021 Lu-Ming Zhang. All rights reserved.
 Released under Apache 2.0 license as described in the file LICENSE.
 Authors: Lu-Ming Zhang
-
-! This file was ported from Lean 3 source module linear_algebra.matrix.symmetric
-! 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.Block
 
+#align_import linear_algebra.matrix.symmetric from "leanprover-community/mathlib"@"d64d67d000b974f0d86a2be7918cf800be6271c8"
+
 /-!
 # Symmetric matrices
 

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

@@ -68,28 +68,38 @@ theorem IsSymm.apply {A : Matrix n n α} (h : A.IsSymm) (i j : n) : A j i = A i
 #align matrix.is_symm.apply Matrix.IsSymm.apply
 -/
 
+#print Matrix.isSymm_mul_transpose_self /-
 theorem isSymm_mul_transpose_self [Fintype n] [CommSemiring α] (A : Matrix n n α) :
     (A ⬝ Aᵀ).IsSymm :=
   transpose_mul _ _
 #align matrix.is_symm_mul_transpose_self Matrix.isSymm_mul_transpose_self
+-/
 
+#print Matrix.isSymm_transpose_mul_self /-
 theorem isSymm_transpose_mul_self [Fintype n] [CommSemiring α] (A : Matrix n n α) :
     (Aᵀ ⬝ A).IsSymm :=
   transpose_mul _ _
 #align matrix.is_symm_transpose_mul_self Matrix.isSymm_transpose_mul_self
+-/
 
+#print Matrix.isSymm_add_transpose_self /-
 theorem isSymm_add_transpose_self [AddCommSemigroup α] (A : Matrix n n α) : (A + Aᵀ).IsSymm :=
   add_comm _ _
 #align matrix.is_symm_add_transpose_self Matrix.isSymm_add_transpose_self
+-/
 
+#print Matrix.isSymm_transpose_add_self /-
 theorem isSymm_transpose_add_self [AddCommSemigroup α] (A : Matrix n n α) : (Aᵀ + A).IsSymm :=
   add_comm _ _
 #align matrix.is_symm_transpose_add_self Matrix.isSymm_transpose_add_self
+-/
 
+#print Matrix.isSymm_zero /-
 @[simp]
 theorem isSymm_zero [Zero α] : (0 : Matrix n n α).IsSymm :=
   transpose_zero
 #align matrix.is_symm_zero Matrix.isSymm_zero
+-/
 
 #print Matrix.isSymm_one /-
 @[simp]
@@ -98,10 +108,12 @@ theorem isSymm_one [DecidableEq n] [Zero α] [One α] : (1 : Matrix n n α).IsSy
 #align matrix.is_symm_one Matrix.isSymm_one
 -/
 
+#print Matrix.IsSymm.map /-
 @[simp]
 theorem IsSymm.map {A : Matrix n n α} (h : A.IsSymm) (f : α → β) : (A.map f).IsSymm :=
   transpose_map.symm.trans (h.symm ▸ rfl)
 #align matrix.is_symm.map Matrix.IsSymm.map
+-/
 
 #print Matrix.IsSymm.transpose /-
 @[simp]
@@ -110,15 +122,19 @@ theorem IsSymm.transpose {A : Matrix n n α} (h : A.IsSymm) : Aᵀ.IsSymm :=
 #align matrix.is_symm.transpose Matrix.IsSymm.transpose
 -/
 
+#print Matrix.IsSymm.conjTranspose /-
 @[simp]
 theorem IsSymm.conjTranspose [Star α] {A : Matrix n n α} (h : A.IsSymm) : Aᴴ.IsSymm :=
   h.transpose.map _
 #align matrix.is_symm.conj_transpose Matrix.IsSymm.conjTranspose
+-/
 
+#print Matrix.IsSymm.neg /-
 @[simp]
 theorem IsSymm.neg [Neg α] {A : Matrix n n α} (h : A.IsSymm) : (-A).IsSymm :=
   (transpose_neg _).trans (congr_arg _ h)
 #align matrix.is_symm.neg Matrix.IsSymm.neg
+-/
 
 #print Matrix.IsSymm.add /-
 @[simp]
@@ -134,15 +150,19 @@ theorem IsSymm.sub {A B : Matrix n n α} [Sub α] (hA : A.IsSymm) (hB : B.IsSymm
 #align matrix.is_symm.sub Matrix.IsSymm.sub
 -/
 
+#print Matrix.IsSymm.smul /-
 @[simp]
 theorem IsSymm.smul [SMul R α] {A : Matrix n n α} (h : A.IsSymm) (k : R) : (k • A).IsSymm :=
   (transpose_smul _ _).trans (congr_arg _ h)
 #align matrix.is_symm.smul Matrix.IsSymm.smul
+-/
 
+#print Matrix.IsSymm.submatrix /-
 @[simp]
 theorem IsSymm.submatrix {A : Matrix n n α} (h : A.IsSymm) (f : m → n) : (A.submatrix f f).IsSymm :=
   (transpose_submatrix _ _ _).trans (h.symm ▸ rfl)
 #align matrix.is_symm.submatrix Matrix.IsSymm.submatrix
+-/
 
 #print Matrix.isSymm_diagonal /-
 /-- The diagonal matrix `diagonal v` is symmetric. -/
@@ -152,6 +172,7 @@ theorem isSymm_diagonal [DecidableEq n] [Zero α] (v : n → α) : (diagonal v).
 #align matrix.is_symm_diagonal Matrix.isSymm_diagonal
 -/
 
+#print Matrix.IsSymm.fromBlocks /-
 /-- A block matrix `A.from_blocks B C D` is symmetric,
     if `A` and `D` are symmetric and `Bᵀ = C`. -/
 theorem IsSymm.fromBlocks {A : Matrix m m α} {B : Matrix m n α} {C : Matrix n m α}
@@ -163,7 +184,9 @@ theorem IsSymm.fromBlocks {A : Matrix m m α} {B : Matrix m n α} {C : Matrix n
   rw [from_blocks_transpose]
   congr <;> assumption
 #align matrix.is_symm.from_blocks Matrix.IsSymm.fromBlocks
+-/
 
+#print Matrix.isSymm_fromBlocks_iff /-
 /-- This is the `iff` version of `matrix.is_symm.from_blocks`. -/
 theorem isSymm_fromBlocks_iff {A : Matrix m m α} {B : Matrix m n α} {C : Matrix n m α}
     {D : Matrix n n α} : (A.fromBlocks B C D).IsSymm ↔ A.IsSymm ∧ Bᵀ = C ∧ Cᵀ = B ∧ D.IsSymm :=
@@ -172,6 +195,7 @@ theorem isSymm_fromBlocks_iff {A : Matrix m m α} {B : Matrix m n α} {C : Matri
       (congr_arg toBlocks₂₂ h : _)⟩,
     fun ⟨hA, hBC, hCB, hD⟩ => IsSymm.fromBlocks hA hBC hD⟩
 #align matrix.is_symm_from_blocks_iff Matrix.isSymm_fromBlocks_iff
+-/
 
 end Matrix
 

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

@@ -32,7 +32,7 @@ variable {α β n m R : Type _}
 
 namespace Matrix
 
-open Matrix
+open scoped Matrix
 
 #print Matrix.IsSymm /-
 /-- A matrix `A : matrix n n α` is "symmetric" if `Aᵀ = A`. -/

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

@@ -68,54 +68,24 @@ theorem IsSymm.apply {A : Matrix n n α} (h : A.IsSymm) (i j : n) : A j i = A i
 #align matrix.is_symm.apply Matrix.IsSymm.apply
 -/
 
-/- warning: matrix.is_symm_mul_transpose_self -> Matrix.isSymm_mul_transpose_self 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.is_symm_mul_transpose_self Matrix.isSymm_mul_transpose_selfₓ'. -/
 theorem isSymm_mul_transpose_self [Fintype n] [CommSemiring α] (A : Matrix n n α) :
     (A ⬝ Aᵀ).IsSymm :=
   transpose_mul _ _
 #align matrix.is_symm_mul_transpose_self Matrix.isSymm_mul_transpose_self
 
-/- warning: matrix.is_symm_transpose_mul_self -> Matrix.isSymm_transpose_mul_self 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.is_symm_transpose_mul_self Matrix.isSymm_transpose_mul_selfₓ'. -/
 theorem isSymm_transpose_mul_self [Fintype n] [CommSemiring α] (A : Matrix n n α) :
     (Aᵀ ⬝ A).IsSymm :=
   transpose_mul _ _
 #align matrix.is_symm_transpose_mul_self Matrix.isSymm_transpose_mul_self
 
-/- warning: matrix.is_symm_add_transpose_self -> Matrix.isSymm_add_transpose_self is a dubious translation:
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-but is expected to have type
-  forall {α : Type.{u2}} {n : Type.{u1}} [_inst_1 : AddCommSemigroup.{u2} α] (A : Matrix.{u1, u1, u2} n n α), Matrix.IsSymm.{u2, u1} α n (HAdd.hAdd.{max u2 u1, max u2 u1, max u2 u1} (Matrix.{u1, u1, u2} n n α) (Matrix.{u1, u1, u2} n n α) (Matrix.{u1, u1, u2} n n α) (instHAdd.{max u2 u1} (Matrix.{u1, u1, u2} n n α) (Matrix.add.{u2, u1, u1} n n α (AddSemigroup.toAdd.{u2} α (AddCommSemigroup.toAddSemigroup.{u2} α _inst_1)))) A (Matrix.transpose.{u2, u1, u1} n n α A))
-Case conversion may be inaccurate. Consider using '#align matrix.is_symm_add_transpose_self Matrix.isSymm_add_transpose_selfₓ'. -/
 theorem isSymm_add_transpose_self [AddCommSemigroup α] (A : Matrix n n α) : (A + Aᵀ).IsSymm :=
   add_comm _ _
 #align matrix.is_symm_add_transpose_self Matrix.isSymm_add_transpose_self
 
-/- warning: matrix.is_symm_transpose_add_self -> Matrix.isSymm_transpose_add_self is a dubious translation:
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-Case conversion may be inaccurate. Consider using '#align matrix.is_symm_transpose_add_self Matrix.isSymm_transpose_add_selfₓ'. -/
 theorem isSymm_transpose_add_self [AddCommSemigroup α] (A : Matrix n n α) : (Aᵀ + A).IsSymm :=
   add_comm _ _
 #align matrix.is_symm_transpose_add_self Matrix.isSymm_transpose_add_self
 
-/- warning: matrix.is_symm_zero -> Matrix.isSymm_zero is a dubious translation:
-lean 3 declaration is
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-Case conversion may be inaccurate. Consider using '#align matrix.is_symm_zero Matrix.isSymm_zeroₓ'. -/
 @[simp]
 theorem isSymm_zero [Zero α] : (0 : Matrix n n α).IsSymm :=
   transpose_zero
@@ -128,12 +98,6 @@ theorem isSymm_one [DecidableEq n] [Zero α] [One α] : (1 : Matrix n n α).IsSy
 #align matrix.is_symm_one Matrix.isSymm_one
 -/
 
-/- warning: matrix.is_symm.map -> Matrix.IsSymm.map is a dubious translation:
-lean 3 declaration is
-  forall {α : Type.{u1}} {β : Type.{u2}} {n : Type.{u3}} {A : Matrix.{u3, u3, u1} n n α}, (Matrix.IsSymm.{u1, u3} α n A) -> (forall (f : α -> β), Matrix.IsSymm.{u2, u3} β n (Matrix.map.{u1, u2, u3, u3} n n α β A f))
-but is expected to have type
-  forall {α : Type.{u2}} {β : Type.{u1}} {n : Type.{u3}} {A : Matrix.{u3, u3, u2} n n α}, (Matrix.IsSymm.{u2, u3} α n A) -> (forall (f : α -> β), Matrix.IsSymm.{u1, u3} β n (Matrix.map.{u2, u1, u3, u3} n n α β A f))
-Case conversion may be inaccurate. Consider using '#align matrix.is_symm.map Matrix.IsSymm.mapₓ'. -/
 @[simp]
 theorem IsSymm.map {A : Matrix n n α} (h : A.IsSymm) (f : α → β) : (A.map f).IsSymm :=
   transpose_map.symm.trans (h.symm ▸ rfl)
@@ -146,23 +110,11 @@ theorem IsSymm.transpose {A : Matrix n n α} (h : A.IsSymm) : Aᵀ.IsSymm :=
 #align matrix.is_symm.transpose Matrix.IsSymm.transpose
 -/
 
-/- warning: matrix.is_symm.conj_transpose -> Matrix.IsSymm.conjTranspose is a dubious translation:
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-Case conversion may be inaccurate. Consider using '#align matrix.is_symm.conj_transpose Matrix.IsSymm.conjTransposeₓ'. -/
 @[simp]
 theorem IsSymm.conjTranspose [Star α] {A : Matrix n n α} (h : A.IsSymm) : Aᴴ.IsSymm :=
   h.transpose.map _
 #align matrix.is_symm.conj_transpose Matrix.IsSymm.conjTranspose
 
-/- warning: matrix.is_symm.neg -> Matrix.IsSymm.neg is a dubious translation:
-lean 3 declaration is
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-but is expected to have type
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-Case conversion may be inaccurate. Consider using '#align matrix.is_symm.neg Matrix.IsSymm.negₓ'. -/
 @[simp]
 theorem IsSymm.neg [Neg α] {A : Matrix n n α} (h : A.IsSymm) : (-A).IsSymm :=
   (transpose_neg _).trans (congr_arg _ h)
@@ -182,23 +134,11 @@ theorem IsSymm.sub {A B : Matrix n n α} [Sub α] (hA : A.IsSymm) (hB : B.IsSymm
 #align matrix.is_symm.sub Matrix.IsSymm.sub
 -/
 
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-Case conversion may be inaccurate. Consider using '#align matrix.is_symm.smul Matrix.IsSymm.smulₓ'. -/
 @[simp]
 theorem IsSymm.smul [SMul R α] {A : Matrix n n α} (h : A.IsSymm) (k : R) : (k • A).IsSymm :=
   (transpose_smul _ _).trans (congr_arg _ h)
 #align matrix.is_symm.smul Matrix.IsSymm.smul
 
-/- warning: matrix.is_symm.submatrix -> Matrix.IsSymm.submatrix is a dubious translation:
-lean 3 declaration is
-  forall {α : Type.{u1}} {n : Type.{u2}} {m : Type.{u3}} {A : Matrix.{u2, u2, u1} n n α}, (Matrix.IsSymm.{u1, u2} α n A) -> (forall (f : m -> n), Matrix.IsSymm.{u1, u3} α m (Matrix.submatrix.{u1, u3, u2, u2, u3} m n n m α A f f))
-but is expected to have type
-  forall {α : Type.{u2}} {n : Type.{u3}} {m : Type.{u1}} {A : Matrix.{u3, u3, u2} n n α}, (Matrix.IsSymm.{u2, u3} α n A) -> (forall (f : m -> n), Matrix.IsSymm.{u2, u1} α m (Matrix.submatrix.{u2, u1, u3, u3, u1} m n n m α A f f))
-Case conversion may be inaccurate. Consider using '#align matrix.is_symm.submatrix Matrix.IsSymm.submatrixₓ'. -/
 @[simp]
 theorem IsSymm.submatrix {A : Matrix n n α} (h : A.IsSymm) (f : m → n) : (A.submatrix f f).IsSymm :=
   (transpose_submatrix _ _ _).trans (h.symm ▸ rfl)
@@ -212,12 +152,6 @@ theorem isSymm_diagonal [DecidableEq n] [Zero α] (v : n → α) : (diagonal v).
 #align matrix.is_symm_diagonal Matrix.isSymm_diagonal
 -/
 
-/- warning: matrix.is_symm.from_blocks -> Matrix.IsSymm.fromBlocks is a dubious translation:
-lean 3 declaration is
-  forall {α : Type.{u1}} {n : Type.{u2}} {m : Type.{u3}} {A : Matrix.{u3, u3, u1} m m α} {B : Matrix.{u3, u2, u1} m n α} {C : Matrix.{u2, u3, u1} n m α} {D : Matrix.{u2, u2, u1} n n α}, (Matrix.IsSymm.{u1, u3} α m A) -> (Eq.{succ (max u2 u3 u1)} (Matrix.{u2, u3, u1} n m α) (Matrix.transpose.{u1, u3, u2} m n α B) C) -> (Matrix.IsSymm.{u1, u2} α n D) -> (Matrix.IsSymm.{u1, max u3 u2} α (Sum.{u3, u2} m n) (Matrix.fromBlocks.{u3, u2, u3, u2, u1} m n m n α A B C D))
-but is expected to have type
-  forall {α : Type.{u2}} {n : Type.{u1}} {m : Type.{u3}} {A : Matrix.{u3, u3, u2} m m α} {B : Matrix.{u3, u1, u2} m n α} {C : Matrix.{u1, u3, u2} n m α} {D : Matrix.{u1, u1, u2} n n α}, (Matrix.IsSymm.{u2, u3} α m A) -> (Eq.{max (max (succ u2) (succ u1)) (succ u3)} (Matrix.{u1, u3, u2} n m α) (Matrix.transpose.{u2, u3, u1} m n α B) C) -> (Matrix.IsSymm.{u2, u1} α n D) -> (Matrix.IsSymm.{u2, max u1 u3} α (Sum.{u3, u1} m n) (Matrix.fromBlocks.{u3, u1, u3, u1, u2} m n m n α A B C D))
-Case conversion may be inaccurate. Consider using '#align matrix.is_symm.from_blocks Matrix.IsSymm.fromBlocksₓ'. -/
 /-- A block matrix `A.from_blocks B C D` is symmetric,
     if `A` and `D` are symmetric and `Bᵀ = C`. -/
 theorem IsSymm.fromBlocks {A : Matrix m m α} {B : Matrix m n α} {C : Matrix n m α}
@@ -230,12 +164,6 @@ theorem IsSymm.fromBlocks {A : Matrix m m α} {B : Matrix m n α} {C : Matrix n
   congr <;> assumption
 #align matrix.is_symm.from_blocks Matrix.IsSymm.fromBlocks
 
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-Case conversion may be inaccurate. Consider using '#align matrix.is_symm_from_blocks_iff Matrix.isSymm_fromBlocks_iffₓ'. -/
 /-- This is the `iff` version of `matrix.is_symm.from_blocks`. -/
 theorem isSymm_fromBlocks_iff {A : Matrix m m α} {B : Matrix m n α} {C : Matrix n m α}
     {D : Matrix n n α} : (A.fromBlocks B C D).IsSymm ↔ A.IsSymm ∧ Bᵀ = C ∧ Cᵀ = B ∧ D.IsSymm :=

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

@@ -224,9 +224,7 @@ theorem IsSymm.fromBlocks {A : Matrix m m α} {B : Matrix m n α} {C : Matrix n
     {D : Matrix n n α} (hA : A.IsSymm) (hBC : Bᵀ = C) (hD : D.IsSymm) :
     (A.fromBlocks B C D).IsSymm :=
   by
-  have hCB : Cᵀ = B := by
-    rw [← hBC]
-    simp
+  have hCB : Cᵀ = B := by rw [← hBC]; simp
   unfold Matrix.IsSymm
   rw [from_blocks_transpose]
   congr <;> assumption

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

@@ -4,7 +4,7 @@ Released under Apache 2.0 license as described in the file LICENSE.
 Authors: Lu-Ming Zhang
 
 ! This file was ported from Lean 3 source module linear_algebra.matrix.symmetric
-! leanprover-community/mathlib commit 3e068ece210655b7b9a9477c3aff38a492400aa1
+! 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.Block
 /-!
 # Symmetric matrices
 
+> THIS FILE IS SYNCHRONIZED WITH MATHLIB4.
+> Any changes to this file require a corresponding PR to mathlib4.
+
 This file contains the definition and basic results about symmetric matrices.
 
 ## Main definition

mathlib commit https://github.com/leanprover-community/mathlib/commit/3cacc945118c8c637d89950af01da78307f59325

@@ -31,104 +31,190 @@ namespace Matrix
 
 open Matrix
 
+#print Matrix.IsSymm /-
 /-- A matrix `A : matrix n n α` is "symmetric" if `Aᵀ = A`. -/
 def IsSymm (A : Matrix n n α) : Prop :=
   Aᵀ = A
 #align matrix.is_symm Matrix.IsSymm
+-/
 
+#print Matrix.IsSymm.eq /-
 theorem IsSymm.eq {A : Matrix n n α} (h : A.IsSymm) : Aᵀ = A :=
   h
 #align matrix.is_symm.eq Matrix.IsSymm.eq
+-/
 
+#print Matrix.IsSymm.ext_iff /-
 /-- A version of `matrix.ext_iff` that unfolds the `matrix.transpose`. -/
 theorem IsSymm.ext_iff {A : Matrix n n α} : A.IsSymm ↔ ∀ i j, A j i = A i j :=
   Matrix.ext_iff.symm
 #align matrix.is_symm.ext_iff Matrix.IsSymm.ext_iff
+-/
 
+#print Matrix.IsSymm.ext /-
 /-- A version of `matrix.ext` that unfolds the `matrix.transpose`. -/
 @[ext]
 theorem IsSymm.ext {A : Matrix n n α} : (∀ i j, A j i = A i j) → A.IsSymm :=
   Matrix.ext
 #align matrix.is_symm.ext Matrix.IsSymm.ext
+-/
 
+#print Matrix.IsSymm.apply /-
 theorem IsSymm.apply {A : Matrix n n α} (h : A.IsSymm) (i j : n) : A j i = A i j :=
   IsSymm.ext_iff.1 h i j
 #align matrix.is_symm.apply Matrix.IsSymm.apply
+-/
 
+/- warning: matrix.is_symm_mul_transpose_self -> Matrix.isSymm_mul_transpose_self is a dubious translation:
+lean 3 declaration is
+  forall {α : Type.{u1}} {n : Type.{u2}} [_inst_1 : Fintype.{u2} n] [_inst_2 : CommSemiring.{u1} α] (A : Matrix.{u2, u2, u1} n n α), Matrix.IsSymm.{u1, u2} α n (Matrix.mul.{u1, u2, u2, u2} n n n α _inst_1 (Distrib.toHasMul.{u1} α (NonUnitalNonAssocSemiring.toDistrib.{u1} α (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} α (Semiring.toNonAssocSemiring.{u1} α (CommSemiring.toSemiring.{u1} α _inst_2))))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} α (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} α (Semiring.toNonAssocSemiring.{u1} α (CommSemiring.toSemiring.{u1} α _inst_2)))) A (Matrix.transpose.{u1, u2, u2} n n α A))
+but is expected to have type
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+Case conversion may be inaccurate. Consider using '#align matrix.is_symm_mul_transpose_self Matrix.isSymm_mul_transpose_selfₓ'. -/
 theorem isSymm_mul_transpose_self [Fintype n] [CommSemiring α] (A : Matrix n n α) :
     (A ⬝ Aᵀ).IsSymm :=
   transpose_mul _ _
 #align matrix.is_symm_mul_transpose_self Matrix.isSymm_mul_transpose_self
 
+/- warning: matrix.is_symm_transpose_mul_self -> Matrix.isSymm_transpose_mul_self is a dubious translation:
+lean 3 declaration is
+  forall {α : Type.{u1}} {n : Type.{u2}} [_inst_1 : Fintype.{u2} n] [_inst_2 : CommSemiring.{u1} α] (A : Matrix.{u2, u2, u1} n n α), Matrix.IsSymm.{u1, u2} α n (Matrix.mul.{u1, u2, u2, u2} n n n α _inst_1 (Distrib.toHasMul.{u1} α (NonUnitalNonAssocSemiring.toDistrib.{u1} α (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} α (Semiring.toNonAssocSemiring.{u1} α (CommSemiring.toSemiring.{u1} α _inst_2))))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} α (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} α (Semiring.toNonAssocSemiring.{u1} α (CommSemiring.toSemiring.{u1} α _inst_2)))) (Matrix.transpose.{u1, u2, u2} n n α A) A)
+but is expected to have type
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+Case conversion may be inaccurate. Consider using '#align matrix.is_symm_transpose_mul_self Matrix.isSymm_transpose_mul_selfₓ'. -/
 theorem isSymm_transpose_mul_self [Fintype n] [CommSemiring α] (A : Matrix n n α) :
     (Aᵀ ⬝ A).IsSymm :=
   transpose_mul _ _
 #align matrix.is_symm_transpose_mul_self Matrix.isSymm_transpose_mul_self
 
+/- warning: matrix.is_symm_add_transpose_self -> Matrix.isSymm_add_transpose_self is a dubious translation:
+lean 3 declaration is
+  forall {α : Type.{u1}} {n : Type.{u2}} [_inst_1 : AddCommSemigroup.{u1} α] (A : Matrix.{u2, u2, u1} n n α), Matrix.IsSymm.{u1, u2} α n (HAdd.hAdd.{max u2 u1, max u2 u1, max u2 u1} (Matrix.{u2, u2, u1} n n α) (Matrix.{u2, u2, u1} n n α) (Matrix.{u2, u2, u1} n n α) (instHAdd.{max u2 u1} (Matrix.{u2, u2, u1} n n α) (Matrix.hasAdd.{u1, u2, u2} n n α (AddSemigroup.toHasAdd.{u1} α (AddCommSemigroup.toAddSemigroup.{u1} α _inst_1)))) A (Matrix.transpose.{u1, u2, u2} n n α A))
+but is expected to have type
+  forall {α : Type.{u2}} {n : Type.{u1}} [_inst_1 : AddCommSemigroup.{u2} α] (A : Matrix.{u1, u1, u2} n n α), Matrix.IsSymm.{u2, u1} α n (HAdd.hAdd.{max u2 u1, max u2 u1, max u2 u1} (Matrix.{u1, u1, u2} n n α) (Matrix.{u1, u1, u2} n n α) (Matrix.{u1, u1, u2} n n α) (instHAdd.{max u2 u1} (Matrix.{u1, u1, u2} n n α) (Matrix.add.{u2, u1, u1} n n α (AddSemigroup.toAdd.{u2} α (AddCommSemigroup.toAddSemigroup.{u2} α _inst_1)))) A (Matrix.transpose.{u2, u1, u1} n n α A))
+Case conversion may be inaccurate. Consider using '#align matrix.is_symm_add_transpose_self Matrix.isSymm_add_transpose_selfₓ'. -/
 theorem isSymm_add_transpose_self [AddCommSemigroup α] (A : Matrix n n α) : (A + Aᵀ).IsSymm :=
   add_comm _ _
 #align matrix.is_symm_add_transpose_self Matrix.isSymm_add_transpose_self
 
+/- warning: matrix.is_symm_transpose_add_self -> Matrix.isSymm_transpose_add_self is a dubious translation:
+lean 3 declaration is
+  forall {α : Type.{u1}} {n : Type.{u2}} [_inst_1 : AddCommSemigroup.{u1} α] (A : Matrix.{u2, u2, u1} n n α), Matrix.IsSymm.{u1, u2} α n (HAdd.hAdd.{max u2 u1, max u2 u1, max u2 u1} (Matrix.{u2, u2, u1} n n α) (Matrix.{u2, u2, u1} n n α) (Matrix.{u2, u2, u1} n n α) (instHAdd.{max u2 u1} (Matrix.{u2, u2, u1} n n α) (Matrix.hasAdd.{u1, u2, u2} n n α (AddSemigroup.toHasAdd.{u1} α (AddCommSemigroup.toAddSemigroup.{u1} α _inst_1)))) (Matrix.transpose.{u1, u2, u2} n n α A) A)
+but is expected to have type
+  forall {α : Type.{u2}} {n : Type.{u1}} [_inst_1 : AddCommSemigroup.{u2} α] (A : Matrix.{u1, u1, u2} n n α), Matrix.IsSymm.{u2, u1} α n (HAdd.hAdd.{max u2 u1, max u2 u1, max u2 u1} (Matrix.{u1, u1, u2} n n α) (Matrix.{u1, u1, u2} n n α) (Matrix.{u1, u1, u2} n n α) (instHAdd.{max u2 u1} (Matrix.{u1, u1, u2} n n α) (Matrix.add.{u2, u1, u1} n n α (AddSemigroup.toAdd.{u2} α (AddCommSemigroup.toAddSemigroup.{u2} α _inst_1)))) (Matrix.transpose.{u2, u1, u1} n n α A) A)
+Case conversion may be inaccurate. Consider using '#align matrix.is_symm_transpose_add_self Matrix.isSymm_transpose_add_selfₓ'. -/
 theorem isSymm_transpose_add_self [AddCommSemigroup α] (A : Matrix n n α) : (Aᵀ + A).IsSymm :=
   add_comm _ _
 #align matrix.is_symm_transpose_add_self Matrix.isSymm_transpose_add_self
 
+/- warning: matrix.is_symm_zero -> Matrix.isSymm_zero is a dubious translation:
+lean 3 declaration is
+  forall {α : Type.{u1}} {n : Type.{u2}} [_inst_1 : Zero.{u1} α], Matrix.IsSymm.{u1, u2} α n (OfNat.ofNat.{max u2 u1} (Matrix.{u2, u2, u1} n n α) 0 (OfNat.mk.{max u2 u1} (Matrix.{u2, u2, u1} n n α) 0 (Zero.zero.{max u2 u1} (Matrix.{u2, u2, u1} n n α) (Matrix.hasZero.{u1, u2, u2} n n α _inst_1))))
+but is expected to have type
+  forall {α : Type.{u2}} {n : Type.{u1}} [_inst_1 : Zero.{u2} α], Matrix.IsSymm.{u2, u1} α n (OfNat.ofNat.{max u2 u1} (Matrix.{u1, u1, u2} n n α) 0 (Zero.toOfNat0.{max u2 u1} (Matrix.{u1, u1, u2} n n α) (Matrix.zero.{u2, u1, u1} n n α _inst_1)))
+Case conversion may be inaccurate. Consider using '#align matrix.is_symm_zero Matrix.isSymm_zeroₓ'. -/
 @[simp]
 theorem isSymm_zero [Zero α] : (0 : Matrix n n α).IsSymm :=
   transpose_zero
 #align matrix.is_symm_zero Matrix.isSymm_zero
 
+#print Matrix.isSymm_one /-
 @[simp]
 theorem isSymm_one [DecidableEq n] [Zero α] [One α] : (1 : Matrix n n α).IsSymm :=
   transpose_one
 #align matrix.is_symm_one Matrix.isSymm_one
+-/
 
+/- warning: matrix.is_symm.map -> Matrix.IsSymm.map is a dubious translation:
+lean 3 declaration is
+  forall {α : Type.{u1}} {β : Type.{u2}} {n : Type.{u3}} {A : Matrix.{u3, u3, u1} n n α}, (Matrix.IsSymm.{u1, u3} α n A) -> (forall (f : α -> β), Matrix.IsSymm.{u2, u3} β n (Matrix.map.{u1, u2, u3, u3} n n α β A f))
+but is expected to have type
+  forall {α : Type.{u2}} {β : Type.{u1}} {n : Type.{u3}} {A : Matrix.{u3, u3, u2} n n α}, (Matrix.IsSymm.{u2, u3} α n A) -> (forall (f : α -> β), Matrix.IsSymm.{u1, u3} β n (Matrix.map.{u2, u1, u3, u3} n n α β A f))
+Case conversion may be inaccurate. Consider using '#align matrix.is_symm.map Matrix.IsSymm.mapₓ'. -/
 @[simp]
 theorem IsSymm.map {A : Matrix n n α} (h : A.IsSymm) (f : α → β) : (A.map f).IsSymm :=
   transpose_map.symm.trans (h.symm ▸ rfl)
 #align matrix.is_symm.map Matrix.IsSymm.map
 
+#print Matrix.IsSymm.transpose /-
 @[simp]
 theorem IsSymm.transpose {A : Matrix n n α} (h : A.IsSymm) : Aᵀ.IsSymm :=
   congr_arg _ h
 #align matrix.is_symm.transpose Matrix.IsSymm.transpose
+-/
 
+/- warning: matrix.is_symm.conj_transpose -> Matrix.IsSymm.conjTranspose is a dubious translation:
+lean 3 declaration is
+  forall {α : Type.{u1}} {n : Type.{u2}} [_inst_1 : Star.{u1} α] {A : Matrix.{u2, u2, u1} n n α}, (Matrix.IsSymm.{u1, u2} α n A) -> (Matrix.IsSymm.{u1, u2} α n (Matrix.conjTranspose.{u1, u2, u2} n n α _inst_1 A))
+but is expected to have type
+  forall {α : Type.{u2}} {n : Type.{u1}} [_inst_1 : Star.{u2} α] {A : Matrix.{u1, u1, u2} n n α}, (Matrix.IsSymm.{u2, u1} α n A) -> (Matrix.IsSymm.{u2, u1} α n (Matrix.conjTranspose.{u2, u1, u1} n n α _inst_1 A))
+Case conversion may be inaccurate. Consider using '#align matrix.is_symm.conj_transpose Matrix.IsSymm.conjTransposeₓ'. -/
 @[simp]
 theorem IsSymm.conjTranspose [Star α] {A : Matrix n n α} (h : A.IsSymm) : Aᴴ.IsSymm :=
   h.transpose.map _
 #align matrix.is_symm.conj_transpose Matrix.IsSymm.conjTranspose
 
+/- warning: matrix.is_symm.neg -> Matrix.IsSymm.neg is a dubious translation:
+lean 3 declaration is
+  forall {α : Type.{u1}} {n : Type.{u2}} [_inst_1 : Neg.{u1} α] {A : Matrix.{u2, u2, u1} n n α}, (Matrix.IsSymm.{u1, u2} α n A) -> (Matrix.IsSymm.{u1, u2} α n (Neg.neg.{max u2 u1} (Matrix.{u2, u2, u1} n n α) (Matrix.hasNeg.{u1, u2, u2} n n α _inst_1) A))
+but is expected to have type
+  forall {α : Type.{u2}} {n : Type.{u1}} [_inst_1 : Neg.{u2} α] {A : Matrix.{u1, u1, u2} n n α}, (Matrix.IsSymm.{u2, u1} α n A) -> (Matrix.IsSymm.{u2, u1} α n (Neg.neg.{max u2 u1} (Matrix.{u1, u1, u2} n n α) (Matrix.neg.{u2, u1, u1} n n α _inst_1) A))
+Case conversion may be inaccurate. Consider using '#align matrix.is_symm.neg Matrix.IsSymm.negₓ'. -/
 @[simp]
 theorem IsSymm.neg [Neg α] {A : Matrix n n α} (h : A.IsSymm) : (-A).IsSymm :=
   (transpose_neg _).trans (congr_arg _ h)
 #align matrix.is_symm.neg Matrix.IsSymm.neg
 
+#print Matrix.IsSymm.add /-
 @[simp]
 theorem IsSymm.add {A B : Matrix n n α} [Add α] (hA : A.IsSymm) (hB : B.IsSymm) : (A + B).IsSymm :=
   (transpose_add _ _).trans (hA.symm ▸ hB.symm ▸ rfl)
 #align matrix.is_symm.add Matrix.IsSymm.add
+-/
 
+#print Matrix.IsSymm.sub /-
 @[simp]
 theorem IsSymm.sub {A B : Matrix n n α} [Sub α] (hA : A.IsSymm) (hB : B.IsSymm) : (A - B).IsSymm :=
   (transpose_sub _ _).trans (hA.symm ▸ hB.symm ▸ rfl)
 #align matrix.is_symm.sub Matrix.IsSymm.sub
+-/
 
+/- warning: matrix.is_symm.smul -> Matrix.IsSymm.smul is a dubious translation:
+lean 3 declaration is
+  forall {α : Type.{u1}} {n : Type.{u2}} {R : Type.{u3}} [_inst_1 : SMul.{u3, u1} R α] {A : Matrix.{u2, u2, u1} n n α}, (Matrix.IsSymm.{u1, u2} α n A) -> (forall (k : R), Matrix.IsSymm.{u1, u2} α n (SMul.smul.{u3, max u2 u1} R (Matrix.{u2, u2, u1} n n α) (Matrix.hasSmul.{u1, u2, u2, u3} n n R α _inst_1) k A))
+but is expected to have type
+  forall {α : Type.{u2}} {n : Type.{u1}} {R : Type.{u3}} [_inst_1 : SMul.{u3, u2} R α] {A : Matrix.{u1, u1, u2} n n α}, (Matrix.IsSymm.{u2, u1} α n A) -> (forall (k : R), Matrix.IsSymm.{u2, u1} α n (HSMul.hSMul.{u3, max u2 u1, max u2 u1} R (Matrix.{u1, u1, u2} n n α) (Matrix.{u1, u1, u2} n n α) (instHSMul.{u3, max u2 u1} R (Matrix.{u1, u1, u2} n n α) (Matrix.smul.{u2, u1, u1, u3} n n R α _inst_1)) k A))
+Case conversion may be inaccurate. Consider using '#align matrix.is_symm.smul Matrix.IsSymm.smulₓ'. -/
 @[simp]
 theorem IsSymm.smul [SMul R α] {A : Matrix n n α} (h : A.IsSymm) (k : R) : (k • A).IsSymm :=
   (transpose_smul _ _).trans (congr_arg _ h)
 #align matrix.is_symm.smul Matrix.IsSymm.smul
 
+/- warning: matrix.is_symm.submatrix -> Matrix.IsSymm.submatrix is a dubious translation:
+lean 3 declaration is
+  forall {α : Type.{u1}} {n : Type.{u2}} {m : Type.{u3}} {A : Matrix.{u2, u2, u1} n n α}, (Matrix.IsSymm.{u1, u2} α n A) -> (forall (f : m -> n), Matrix.IsSymm.{u1, u3} α m (Matrix.submatrix.{u1, u3, u2, u2, u3} m n n m α A f f))
+but is expected to have type
+  forall {α : Type.{u2}} {n : Type.{u3}} {m : Type.{u1}} {A : Matrix.{u3, u3, u2} n n α}, (Matrix.IsSymm.{u2, u3} α n A) -> (forall (f : m -> n), Matrix.IsSymm.{u2, u1} α m (Matrix.submatrix.{u2, u1, u3, u3, u1} m n n m α A f f))
+Case conversion may be inaccurate. Consider using '#align matrix.is_symm.submatrix Matrix.IsSymm.submatrixₓ'. -/
 @[simp]
 theorem IsSymm.submatrix {A : Matrix n n α} (h : A.IsSymm) (f : m → n) : (A.submatrix f f).IsSymm :=
   (transpose_submatrix _ _ _).trans (h.symm ▸ rfl)
 #align matrix.is_symm.submatrix Matrix.IsSymm.submatrix
 
+#print Matrix.isSymm_diagonal /-
 /-- The diagonal matrix `diagonal v` is symmetric. -/
 @[simp]
 theorem isSymm_diagonal [DecidableEq n] [Zero α] (v : n → α) : (diagonal v).IsSymm :=
   diagonal_transpose _
 #align matrix.is_symm_diagonal Matrix.isSymm_diagonal
+-/
 
+/- warning: matrix.is_symm.from_blocks -> Matrix.IsSymm.fromBlocks is a dubious translation:
+lean 3 declaration is
+  forall {α : Type.{u1}} {n : Type.{u2}} {m : Type.{u3}} {A : Matrix.{u3, u3, u1} m m α} {B : Matrix.{u3, u2, u1} m n α} {C : Matrix.{u2, u3, u1} n m α} {D : Matrix.{u2, u2, u1} n n α}, (Matrix.IsSymm.{u1, u3} α m A) -> (Eq.{succ (max u2 u3 u1)} (Matrix.{u2, u3, u1} n m α) (Matrix.transpose.{u1, u3, u2} m n α B) C) -> (Matrix.IsSymm.{u1, u2} α n D) -> (Matrix.IsSymm.{u1, max u3 u2} α (Sum.{u3, u2} m n) (Matrix.fromBlocks.{u3, u2, u3, u2, u1} m n m n α A B C D))
+but is expected to have type
+  forall {α : Type.{u2}} {n : Type.{u1}} {m : Type.{u3}} {A : Matrix.{u3, u3, u2} m m α} {B : Matrix.{u3, u1, u2} m n α} {C : Matrix.{u1, u3, u2} n m α} {D : Matrix.{u1, u1, u2} n n α}, (Matrix.IsSymm.{u2, u3} α m A) -> (Eq.{max (max (succ u2) (succ u1)) (succ u3)} (Matrix.{u1, u3, u2} n m α) (Matrix.transpose.{u2, u3, u1} m n α B) C) -> (Matrix.IsSymm.{u2, u1} α n D) -> (Matrix.IsSymm.{u2, max u1 u3} α (Sum.{u3, u1} m n) (Matrix.fromBlocks.{u3, u1, u3, u1, u2} m n m n α A B C D))
+Case conversion may be inaccurate. Consider using '#align matrix.is_symm.from_blocks Matrix.IsSymm.fromBlocksₓ'. -/
 /-- A block matrix `A.from_blocks B C D` is symmetric,
     if `A` and `D` are symmetric and `Bᵀ = C`. -/
 theorem IsSymm.fromBlocks {A : Matrix m m α} {B : Matrix m n α} {C : Matrix n m α}
@@ -143,6 +229,12 @@ theorem IsSymm.fromBlocks {A : Matrix m m α} {B : Matrix m n α} {C : Matrix n
   congr <;> assumption
 #align matrix.is_symm.from_blocks Matrix.IsSymm.fromBlocks
 
+/- warning: matrix.is_symm_from_blocks_iff -> Matrix.isSymm_fromBlocks_iff is a dubious translation:
+lean 3 declaration is
+  forall {α : Type.{u1}} {n : Type.{u2}} {m : Type.{u3}} {A : Matrix.{u3, u3, u1} m m α} {B : Matrix.{u3, u2, u1} m n α} {C : Matrix.{u2, u3, u1} n m α} {D : Matrix.{u2, u2, u1} n n α}, Iff (Matrix.IsSymm.{u1, max u3 u2} α (Sum.{u3, u2} m n) (Matrix.fromBlocks.{u3, u2, u3, u2, u1} m n m n α A B C D)) (And (Matrix.IsSymm.{u1, u3} α m A) (And (Eq.{succ (max u2 u3 u1)} (Matrix.{u2, u3, u1} n m α) (Matrix.transpose.{u1, u3, u2} m n α B) C) (And (Eq.{succ (max u3 u2 u1)} (Matrix.{u3, u2, u1} m n α) (Matrix.transpose.{u1, u2, u3} n m α C) B) (Matrix.IsSymm.{u1, u2} α n D))))
+but is expected to have type
+  forall {α : Type.{u2}} {n : Type.{u1}} {m : Type.{u3}} {A : Matrix.{u3, u3, u2} m m α} {B : Matrix.{u3, u1, u2} m n α} {C : Matrix.{u1, u3, u2} n m α} {D : Matrix.{u1, u1, u2} n n α}, Iff (Matrix.IsSymm.{u2, max u1 u3} α (Sum.{u3, u1} m n) (Matrix.fromBlocks.{u3, u1, u3, u1, u2} m n m n α A B C D)) (And (Matrix.IsSymm.{u2, u3} α m A) (And (Eq.{max (max (succ u2) (succ u1)) (succ u3)} (Matrix.{u1, u3, u2} n m α) (Matrix.transpose.{u2, u3, u1} m n α B) C) (And (Eq.{max (max (succ u2) (succ u1)) (succ u3)} (Matrix.{u3, u1, u2} m n α) (Matrix.transpose.{u2, u1, u3} n m α C) B) (Matrix.IsSymm.{u2, u1} α n D))))
+Case conversion may be inaccurate. Consider using '#align matrix.is_symm_from_blocks_iff Matrix.isSymm_fromBlocks_iffₓ'. -/
 /-- This is the `iff` version of `matrix.is_symm.from_blocks`. -/
 theorem isSymm_fromBlocks_iff {A : Matrix m m α} {B : Matrix m n α} {C : Matrix n m α}
     {D : Matrix n n α} : (A.fromBlocks B C D).IsSymm ↔ A.IsSymm ∧ Bᵀ = C ∧ Cᵀ = B ∧ D.IsSymm :=

mathlib commit https://github.com/leanprover-community/mathlib/commit/172bf2812857f5e56938cc148b7a539f52f84ca9

@@ -4,7 +4,7 @@ Released under Apache 2.0 license as described in the file LICENSE.
 Authors: Lu-Ming Zhang
 
 ! This file was ported from Lean 3 source module linear_algebra.matrix.symmetric
-! leanprover-community/mathlib commit 55e2dfde0cff928ce5c70926a3f2c7dee3e2dd99
+! leanprover-community/mathlib commit 3e068ece210655b7b9a9477c3aff38a492400aa1
 ! Please do not edit these lines, except to modify the commit id
 ! if you have ported upstream changes.
 -/
@@ -147,8 +147,8 @@ theorem IsSymm.fromBlocks {A : Matrix m m α} {B : Matrix m n α} {C : Matrix n
 theorem isSymm_fromBlocks_iff {A : Matrix m m α} {B : Matrix m n α} {C : Matrix n m α}
     {D : Matrix n n α} : (A.fromBlocks B C D).IsSymm ↔ A.IsSymm ∧ Bᵀ = C ∧ Cᵀ = B ∧ D.IsSymm :=
   ⟨fun h =>
-    ⟨congr_arg toBlocks₁₁ h, congr_arg toBlocks₂₁ h, congr_arg toBlocks₁₂ h,
-      congr_arg toBlocks₂₂ h⟩,
+    ⟨(congr_arg toBlocks₁₁ h : _), (congr_arg toBlocks₂₁ h : _), (congr_arg toBlocks₁₂ h : _),
+      (congr_arg toBlocks₂₂ h : _)⟩,
     fun ⟨hA, hBC, hCB, hD⟩ => IsSymm.fromBlocks hA hBC hD⟩
 #align matrix.is_symm_from_blocks_iff Matrix.isSymm_fromBlocks_iff
 

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

These are stated in the most general form possible, where they simply unfold the definition. This allows a few proofs to be golfed.

@@ -33,6 +33,9 @@ def IsSymm (A : Matrix n n α) : Prop :=
   Aᵀ = A
 #align matrix.is_symm Matrix.IsSymm
 
+instance (A : Matrix n n α) [Decidable (Aᵀ = A)] : Decidable (IsSymm A) :=
+  inferInstanceAs <| Decidable (_ = _)
+
 theorem IsSymm.eq {A : Matrix n n α} (h : A.IsSymm) : Aᵀ = A :=
   h
 #align matrix.is_symm.eq Matrix.IsSymm.eq

The removal of some pointless tactics flagged by #11308.

@@ -140,8 +140,7 @@ theorem IsSymm.fromBlocks {A : Matrix m m α} {B : Matrix m n α} {C : Matrix n
     rw [← hBC]
     simp
   unfold Matrix.IsSymm
-  rw [fromBlocks_transpose]
-  congr; rw [hA, hCB, hBC, hD]
+  rw [fromBlocks_transpose, hA, hCB, hBC, hD]
 #align matrix.is_symm.from_blocks Matrix.IsSymm.fromBlocks
 
 /-- This is the `iff` version of `Matrix.isSymm.fromBlocks`. -/

@@ -80,6 +80,11 @@ theorem isSymm_one [DecidableEq n] [Zero α] [One α] : (1 : Matrix n n α).IsSy
   transpose_one
 #align matrix.is_symm_one Matrix.isSymm_one
 
+theorem IsSymm.pow [CommSemiring α] [Fintype n] [DecidableEq n] {A : Matrix n n α} (h : A.IsSymm)
+    (k : ℕ) :
+    (A ^ k).IsSymm := by
+  rw [IsSymm, transpose_pow, h]
+
 @[simp]
 theorem IsSymm.map {A : Matrix n n α} (h : A.IsSymm) (f : α → β) : (A.map f).IsSymm :=
   transpose_map.symm.trans (h.symm ▸ rfl)

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).

@@ -53,12 +53,12 @@ theorem IsSymm.apply {A : Matrix n n α} (h : A.IsSymm) (i j : n) : A j i = A i
 #align matrix.is_symm.apply Matrix.IsSymm.apply
 
 theorem isSymm_mul_transpose_self [Fintype n] [CommSemiring α] (A : Matrix n n α) :
-    (A ⬝ Aᵀ).IsSymm :=
+    (A * Aᵀ).IsSymm :=
   transpose_mul _ _
 #align matrix.is_symm_mul_transpose_self Matrix.isSymm_mul_transpose_self
 
 theorem isSymm_transpose_mul_self [Fintype n] [CommSemiring α] (A : Matrix n n α) :
-    (Aᵀ ⬝ A).IsSymm :=
+    (Aᵀ * A).IsSymm :=
   transpose_mul _ _
 #align matrix.is_symm_transpose_mul_self Matrix.isSymm_transpose_mul_self
 

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

This has nice performance benefits.

@@ -22,7 +22,7 @@ symm, symmetric, matrix
 -/
 
 
-variable {α β n m R : Type _}
+variable {α β n m R : Type*}
 
 namespace Matrix
 

• depends on: #5966

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

@@ -2,14 +2,11 @@
 Copyright (c) 2021 Lu-Ming Zhang. All rights reserved.
 Released under Apache 2.0 license as described in the file LICENSE.
 Authors: Lu-Ming Zhang
-
-! This file was ported from Lean 3 source module linear_algebra.matrix.symmetric
-! leanprover-community/mathlib commit 3e068ece210655b7b9a9477c3aff38a492400aa1
-! Please do not edit these lines, except to modify the commit id
-! if you have ported upstream changes.
 -/
 import Mathlib.Data.Matrix.Block
 
+#align_import linear_algebra.matrix.symmetric from "leanprover-community/mathlib"@"3e068ece210655b7b9a9477c3aff38a492400aa1"
+
 /-!
 # Symmetric matrices
 

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