analysis.normed_space.matrix_exponential ⟷ Mathlib.Analysis.NormedSpace.MatrixExponential

mathlib commit https://github.com/leanprover-community/mathlib/commit/65a1391a0106c9204fe45bc73a039f056558cb83

@@ -5,7 +5,7 @@ Authors: Eric Wieser
 -/
 import Analysis.NormedSpace.Exponential
 import Analysis.Matrix
-import LinearAlgebra.Matrix.Zpow
+import LinearAlgebra.Matrix.ZPow
 import LinearAlgebra.Matrix.Hermitian
 import LinearAlgebra.Matrix.Symmetric
 import Topology.UniformSpace.Matrix
@@ -174,7 +174,7 @@ end Topological
 
 section Normed
 
-variable [IsROrC 𝕂] [Fintype m] [DecidableEq m] [Fintype n] [DecidableEq n] [∀ i, Fintype (n' i)]
+variable [RCLike 𝕂] [Fintype m] [DecidableEq m] [Fintype n] [DecidableEq n] [∀ i, Fintype (n' i)]
   [∀ i, DecidableEq (n' i)] [NormedRing 𝔸] [NormedAlgebra 𝕂 𝔸] [CompleteSpace 𝔸]
 
 #print Matrix.exp_add_of_commute /-
@@ -244,7 +244,7 @@ end Normed
 
 section NormedComm
 
-variable [IsROrC 𝕂] [Fintype m] [DecidableEq m] [Fintype n] [DecidableEq n] [∀ i, Fintype (n' i)]
+variable [RCLike 𝕂] [Fintype m] [DecidableEq m] [Fintype n] [DecidableEq n] [∀ i, Fintype (n' i)]
   [∀ i, DecidableEq (n' i)] [NormedCommRing 𝔸] [NormedAlgebra 𝕂 𝔸] [CompleteSpace 𝔸]
 
 #print Matrix.exp_neg /-
@@ -263,10 +263,10 @@ theorem exp_zsmul (z : ℤ) (A : Matrix m m 𝔸) :
     NormedSpace.exp 𝕂 (z • A) = NormedSpace.exp 𝕂 A ^ z :=
   by
   obtain ⟨n, rfl | rfl⟩ := z.eq_coe_or_neg
-  · rw [zpow_coe_nat, coe_nat_zsmul, NormedSpace.exp_nsmul]
+  · rw [zpow_natCast, natCast_zsmul, NormedSpace.exp_nsmul]
   · have : IsUnit (NormedSpace.exp 𝕂 A).det :=
       (Matrix.isUnit_iff_isUnit_det _).mp (NormedSpace.isUnit_exp _ _)
-    rw [Matrix.zpow_neg this, zpow_coe_nat, neg_smul, NormedSpace.exp_neg, coe_nat_zsmul,
+    rw [Matrix.zpow_neg this, zpow_natCast, neg_smul, NormedSpace.exp_neg, natCast_zsmul,
       NormedSpace.exp_nsmul]
 #align matrix.exp_zsmul Matrix.exp_zsmul
 -/

mathlib commit https://github.com/leanprover-community/mathlib/commit/65a1391a0106c9204fe45bc73a039f056558cb83

@@ -263,10 +263,10 @@ theorem exp_zsmul (z : ℤ) (A : Matrix m m 𝔸) :
     NormedSpace.exp 𝕂 (z • A) = NormedSpace.exp 𝕂 A ^ z :=
   by
   obtain ⟨n, rfl | rfl⟩ := z.eq_coe_or_neg
-  · rw [zpow_ofNat, coe_nat_zsmul, NormedSpace.exp_nsmul]
+  · rw [zpow_coe_nat, coe_nat_zsmul, NormedSpace.exp_nsmul]
   · have : IsUnit (NormedSpace.exp 𝕂 A).det :=
       (Matrix.isUnit_iff_isUnit_det _).mp (NormedSpace.isUnit_exp _ _)
-    rw [Matrix.zpow_neg this, zpow_ofNat, neg_smul, NormedSpace.exp_neg, coe_nat_zsmul,
+    rw [Matrix.zpow_neg this, zpow_coe_nat, neg_smul, NormedSpace.exp_neg, coe_nat_zsmul,
       NormedSpace.exp_nsmul]
 #align matrix.exp_zsmul Matrix.exp_zsmul
 -/

mathlib commit https://github.com/leanprover-community/mathlib/commit/65a1391a0106c9204fe45bc73a039f056558cb83

@@ -113,35 +113,38 @@ variable [Fintype m] [DecidableEq m] [Fintype n] [DecidableEq n] [∀ i, Fintype
   [Algebra 𝕂 𝔸] [T2Space 𝔸]
 
 #print Matrix.exp_diagonal /-
-theorem exp_diagonal (v : m → 𝔸) : exp 𝕂 (diagonal v) = diagonal (exp 𝕂 v) := by
-  simp_rw [exp_eq_tsum, diagonal_pow, ← diagonal_smul, ← diagonal_tsum]
+theorem exp_diagonal (v : m → 𝔸) :
+    NormedSpace.exp 𝕂 (diagonal v) = diagonal (NormedSpace.exp 𝕂 v) := by
+  simp_rw [NormedSpace.exp_eq_tsum, diagonal_pow, ← diagonal_smul, ← diagonal_tsum]
 #align matrix.exp_diagonal Matrix.exp_diagonal
 -/
 
 #print Matrix.exp_blockDiagonal /-
 theorem exp_blockDiagonal (v : m → Matrix n n 𝔸) :
-    exp 𝕂 (blockDiagonal v) = blockDiagonal (exp 𝕂 v) := by
-  simp_rw [exp_eq_tsum, ← block_diagonal_pow, ← block_diagonal_smul, ← block_diagonal_tsum]
+    NormedSpace.exp 𝕂 (blockDiagonal v) = blockDiagonal (NormedSpace.exp 𝕂 v) := by
+  simp_rw [NormedSpace.exp_eq_tsum, ← block_diagonal_pow, ← block_diagonal_smul, ←
+    block_diagonal_tsum]
 #align matrix.exp_block_diagonal Matrix.exp_blockDiagonal
 -/
 
 #print Matrix.exp_blockDiagonal' /-
 theorem exp_blockDiagonal' (v : ∀ i, Matrix (n' i) (n' i) 𝔸) :
-    exp 𝕂 (blockDiagonal' v) = blockDiagonal' (exp 𝕂 v) := by
-  simp_rw [exp_eq_tsum, ← block_diagonal'_pow, ← block_diagonal'_smul, ← block_diagonal'_tsum]
+    NormedSpace.exp 𝕂 (blockDiagonal' v) = blockDiagonal' (NormedSpace.exp 𝕂 v) := by
+  simp_rw [NormedSpace.exp_eq_tsum, ← block_diagonal'_pow, ← block_diagonal'_smul, ←
+    block_diagonal'_tsum]
 #align matrix.exp_block_diagonal' Matrix.exp_blockDiagonal'
 -/
 
 #print Matrix.exp_conjTranspose /-
 theorem exp_conjTranspose [StarRing 𝔸] [ContinuousStar 𝔸] (A : Matrix m m 𝔸) :
-    exp 𝕂 Aᴴ = (exp 𝕂 A)ᴴ :=
-  (star_exp A).symm
+    NormedSpace.exp 𝕂 Aᴴ = (NormedSpace.exp 𝕂 A)ᴴ :=
+  (NormedSpace.star_exp A).symm
 #align matrix.exp_conj_transpose Matrix.exp_conjTranspose
 -/
 
 #print Matrix.IsHermitian.exp /-
 theorem IsHermitian.exp [StarRing 𝔸] [ContinuousStar 𝔸] {A : Matrix m m 𝔸} (h : A.IsHermitian) :
-    (exp 𝕂 A).IsHermitian :=
+    (NormedSpace.exp 𝕂 A).IsHermitian :=
   (exp_conjTranspose _ _).symm.trans <| congr_arg _ h
 #align matrix.is_hermitian.exp Matrix.IsHermitian.exp
 -/
@@ -154,13 +157,13 @@ variable [Fintype m] [DecidableEq m] [Field 𝕂] [CommRing 𝔸] [TopologicalSp
   [Algebra 𝕂 𝔸] [T2Space 𝔸]
 
 #print Matrix.exp_transpose /-
-theorem exp_transpose (A : Matrix m m 𝔸) : exp 𝕂 Aᵀ = (exp 𝕂 A)ᵀ := by
-  simp_rw [exp_eq_tsum, transpose_tsum, transpose_smul, transpose_pow]
+theorem exp_transpose (A : Matrix m m 𝔸) : NormedSpace.exp 𝕂 Aᵀ = (NormedSpace.exp 𝕂 A)ᵀ := by
+  simp_rw [NormedSpace.exp_eq_tsum, transpose_tsum, transpose_smul, transpose_pow]
 #align matrix.exp_transpose Matrix.exp_transpose
 -/
 
 #print Matrix.IsSymm.exp /-
-theorem IsSymm.exp {A : Matrix m m 𝔸} (h : A.IsSymm) : (exp 𝕂 A).IsSymm :=
+theorem IsSymm.exp {A : Matrix m m 𝔸} (h : A.IsSymm) : (NormedSpace.exp 𝕂 A).IsSymm :=
   (exp_transpose _ _).symm.trans <| congr_arg _ h
 #align matrix.is_symm.exp Matrix.IsSymm.exp
 -/
@@ -176,62 +179,63 @@ variable [IsROrC 𝕂] [Fintype m] [DecidableEq m] [Fintype n] [DecidableEq n] [
 
 #print Matrix.exp_add_of_commute /-
 theorem exp_add_of_commute (A B : Matrix m m 𝔸) (h : Commute A B) :
-    exp 𝕂 (A + B) = exp 𝕂 A ⬝ exp 𝕂 B :=
+    NormedSpace.exp 𝕂 (A + B) = NormedSpace.exp 𝕂 A ⬝ NormedSpace.exp 𝕂 B :=
   by
   letI : SeminormedRing (Matrix m m 𝔸) := Matrix.linftyOpSemiNormedRing
   letI : NormedRing (Matrix m m 𝔸) := Matrix.linftyOpNormedRing
   letI : NormedAlgebra 𝕂 (Matrix m m 𝔸) := Matrix.linftyOpNormedAlgebra
-  exact exp_add_of_commute h
+  exact NormedSpace.exp_add_of_commute h
 #align matrix.exp_add_of_commute Matrix.exp_add_of_commute
 -/
 
 #print Matrix.exp_sum_of_commute /-
 theorem exp_sum_of_commute {ι} (s : Finset ι) (f : ι → Matrix m m 𝔸)
     (h : (s : Set ι).Pairwise fun i j => Commute (f i) (f j)) :
-    exp 𝕂 (∑ i in s, f i) =
-      s.noncommProd (fun i => exp 𝕂 (f i)) fun i hi j hj _ => (h.of_refl hi hj).exp 𝕂 :=
+    NormedSpace.exp 𝕂 (∑ i in s, f i) =
+      s.noncommProd (fun i => NormedSpace.exp 𝕂 (f i)) fun i hi j hj _ => (h.of_refl hi hj).exp 𝕂 :=
   by
   letI : SeminormedRing (Matrix m m 𝔸) := Matrix.linftyOpSemiNormedRing
   letI : NormedRing (Matrix m m 𝔸) := Matrix.linftyOpNormedRing
   letI : NormedAlgebra 𝕂 (Matrix m m 𝔸) := Matrix.linftyOpNormedAlgebra
-  exact exp_sum_of_commute s f h
+  exact NormedSpace.exp_sum_of_commute s f h
 #align matrix.exp_sum_of_commute Matrix.exp_sum_of_commute
 -/
 
 #print Matrix.exp_nsmul /-
-theorem exp_nsmul (n : ℕ) (A : Matrix m m 𝔸) : exp 𝕂 (n • A) = exp 𝕂 A ^ n :=
+theorem exp_nsmul (n : ℕ) (A : Matrix m m 𝔸) :
+    NormedSpace.exp 𝕂 (n • A) = NormedSpace.exp 𝕂 A ^ n :=
   by
   letI : SeminormedRing (Matrix m m 𝔸) := Matrix.linftyOpSemiNormedRing
   letI : NormedRing (Matrix m m 𝔸) := Matrix.linftyOpNormedRing
   letI : NormedAlgebra 𝕂 (Matrix m m 𝔸) := Matrix.linftyOpNormedAlgebra
-  exact exp_nsmul n A
+  exact NormedSpace.exp_nsmul n A
 #align matrix.exp_nsmul Matrix.exp_nsmul
 -/
 
 #print Matrix.isUnit_exp /-
-theorem isUnit_exp (A : Matrix m m 𝔸) : IsUnit (exp 𝕂 A) :=
+theorem isUnit_exp (A : Matrix m m 𝔸) : IsUnit (NormedSpace.exp 𝕂 A) :=
   by
   letI : SeminormedRing (Matrix m m 𝔸) := Matrix.linftyOpSemiNormedRing
   letI : NormedRing (Matrix m m 𝔸) := Matrix.linftyOpNormedRing
   letI : NormedAlgebra 𝕂 (Matrix m m 𝔸) := Matrix.linftyOpNormedAlgebra
-  exact isUnit_exp _ A
+  exact NormedSpace.isUnit_exp _ A
 #align matrix.is_unit_exp Matrix.isUnit_exp
 -/
 
 #print Matrix.exp_units_conj /-
 theorem exp_units_conj (U : (Matrix m m 𝔸)ˣ) (A : Matrix m m 𝔸) :
-    exp 𝕂 (↑U ⬝ A ⬝ ↑U⁻¹ : Matrix m m 𝔸) = ↑U ⬝ exp 𝕂 A ⬝ ↑U⁻¹ :=
+    NormedSpace.exp 𝕂 (↑U ⬝ A ⬝ ↑U⁻¹ : Matrix m m 𝔸) = ↑U ⬝ NormedSpace.exp 𝕂 A ⬝ ↑U⁻¹ :=
   by
   letI : SeminormedRing (Matrix m m 𝔸) := Matrix.linftyOpSemiNormedRing
   letI : NormedRing (Matrix m m 𝔸) := Matrix.linftyOpNormedRing
   letI : NormedAlgebra 𝕂 (Matrix m m 𝔸) := Matrix.linftyOpNormedAlgebra
-  exact exp_units_conj _ U A
+  exact NormedSpace.exp_units_conj _ U A
 #align matrix.exp_units_conj Matrix.exp_units_conj
 -/
 
 #print Matrix.exp_units_conj' /-
 theorem exp_units_conj' (U : (Matrix m m 𝔸)ˣ) (A : Matrix m m 𝔸) :
-    exp 𝕂 (↑U⁻¹ ⬝ A ⬝ U : Matrix m m 𝔸) = ↑U⁻¹ ⬝ exp 𝕂 A ⬝ U :=
+    NormedSpace.exp 𝕂 (↑U⁻¹ ⬝ A ⬝ U : Matrix m m 𝔸) = ↑U⁻¹ ⬝ NormedSpace.exp 𝕂 A ⬝ U :=
   exp_units_conj 𝕂 U⁻¹ A
 #align matrix.exp_units_conj' Matrix.exp_units_conj'
 -/
@@ -244,7 +248,7 @@ variable [IsROrC 𝕂] [Fintype m] [DecidableEq m] [Fintype n] [DecidableEq n] [
   [∀ i, DecidableEq (n' i)] [NormedCommRing 𝔸] [NormedAlgebra 𝕂 𝔸] [CompleteSpace 𝔸]
 
 #print Matrix.exp_neg /-
-theorem exp_neg (A : Matrix m m 𝔸) : exp 𝕂 (-A) = (exp 𝕂 A)⁻¹ :=
+theorem exp_neg (A : Matrix m m 𝔸) : NormedSpace.exp 𝕂 (-A) = (NormedSpace.exp 𝕂 A)⁻¹ :=
   by
   rw [nonsing_inv_eq_ring_inverse]
   letI : SeminormedRing (Matrix m m 𝔸) := Matrix.linftyOpSemiNormedRing
@@ -255,28 +259,31 @@ theorem exp_neg (A : Matrix m m 𝔸) : exp 𝕂 (-A) = (exp 𝕂 A)⁻¹ :=
 -/
 
 #print Matrix.exp_zsmul /-
-theorem exp_zsmul (z : ℤ) (A : Matrix m m 𝔸) : exp 𝕂 (z • A) = exp 𝕂 A ^ z :=
+theorem exp_zsmul (z : ℤ) (A : Matrix m m 𝔸) :
+    NormedSpace.exp 𝕂 (z • A) = NormedSpace.exp 𝕂 A ^ z :=
   by
   obtain ⟨n, rfl | rfl⟩ := z.eq_coe_or_neg
-  · rw [zpow_ofNat, coe_nat_zsmul, exp_nsmul]
-  · have : IsUnit (exp 𝕂 A).det := (Matrix.isUnit_iff_isUnit_det _).mp (isUnit_exp _ _)
-    rw [Matrix.zpow_neg this, zpow_ofNat, neg_smul, exp_neg, coe_nat_zsmul, exp_nsmul]
+  · rw [zpow_ofNat, coe_nat_zsmul, NormedSpace.exp_nsmul]
+  · have : IsUnit (NormedSpace.exp 𝕂 A).det :=
+      (Matrix.isUnit_iff_isUnit_det _).mp (NormedSpace.isUnit_exp _ _)
+    rw [Matrix.zpow_neg this, zpow_ofNat, neg_smul, NormedSpace.exp_neg, coe_nat_zsmul,
+      NormedSpace.exp_nsmul]
 #align matrix.exp_zsmul Matrix.exp_zsmul
 -/
 
 #print Matrix.exp_conj /-
 theorem exp_conj (U : Matrix m m 𝔸) (A : Matrix m m 𝔸) (hy : IsUnit U) :
-    exp 𝕂 (U ⬝ A ⬝ U⁻¹) = U ⬝ exp 𝕂 A ⬝ U⁻¹ :=
+    NormedSpace.exp 𝕂 (U ⬝ A ⬝ U⁻¹) = U ⬝ NormedSpace.exp 𝕂 A ⬝ U⁻¹ :=
   let ⟨u, hu⟩ := hy
-  hu ▸ by simpa only [Matrix.coe_units_inv] using exp_units_conj 𝕂 u A
+  hu ▸ by simpa only [Matrix.coe_units_inv] using NormedSpace.exp_units_conj 𝕂 u A
 #align matrix.exp_conj Matrix.exp_conj
 -/
 
 #print Matrix.exp_conj' /-
 theorem exp_conj' (U : Matrix m m 𝔸) (A : Matrix m m 𝔸) (hy : IsUnit U) :
-    exp 𝕂 (U⁻¹ ⬝ A ⬝ U) = U⁻¹ ⬝ exp 𝕂 A ⬝ U :=
+    NormedSpace.exp 𝕂 (U⁻¹ ⬝ A ⬝ U) = U⁻¹ ⬝ NormedSpace.exp 𝕂 A ⬝ U :=
   let ⟨u, hu⟩ := hy
-  hu ▸ by simpa only [Matrix.coe_units_inv] using exp_units_conj' 𝕂 u A
+  hu ▸ by simpa only [Matrix.coe_units_inv] using NormedSpace.exp_units_conj' 𝕂 u A
 #align matrix.exp_conj' Matrix.exp_conj'
 -/
 

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

@@ -3,12 +3,12 @@ Copyright (c) 2022 Eric Wieser. All rights reserved.
 Released under Apache 2.0 license as described in the file LICENSE.
 Authors: Eric Wieser
 -/
-import Mathbin.Analysis.NormedSpace.Exponential
-import Mathbin.Analysis.Matrix
-import Mathbin.LinearAlgebra.Matrix.Zpow
-import Mathbin.LinearAlgebra.Matrix.Hermitian
-import Mathbin.LinearAlgebra.Matrix.Symmetric
-import Mathbin.Topology.UniformSpace.Matrix
+import Analysis.NormedSpace.Exponential
+import Analysis.Matrix
+import LinearAlgebra.Matrix.Zpow
+import LinearAlgebra.Matrix.Hermitian
+import LinearAlgebra.Matrix.Symmetric
+import Topology.UniformSpace.Matrix
 
 #align_import analysis.normed_space.matrix_exponential from "leanprover-community/mathlib"@"5d0c76894ada7940957143163d7b921345474cbc"
 

mathlib commit https://github.com/leanprover-community/mathlib/commit/32a7e535287f9c73f2e4d2aef306a39190f0b504

@@ -73,38 +73,30 @@ open scoped Matrix BigOperators
 
 section HacksForPiInstanceSearch
 
-#print Function.topologicalRing /-
 /-- A special case of `pi.topological_ring` for when `R` is not dependently typed. -/
 instance Function.topologicalRing (I : Type _) (R : Type _) [NonUnitalRing R] [TopologicalSpace R]
     [TopologicalRing R] : TopologicalRing (I → R) :=
   Pi.instTopologicalRing
 #align function.topological_ring Function.topologicalRing
--/
 
-#print Function.algebraRing /-
 /-- A special case of `function.algebra` for when A is a `ring` not a `semiring` -/
 instance Function.algebraRing (I : Type _) {R : Type _} (A : Type _) [CommSemiring R] [Ring A]
     [Algebra R A] : Algebra R (I → A) :=
   Pi.algebra _ _
 #align function.algebra_ring Function.algebraRing
--/
 
-#print Pi.matrixAlgebra /-
 /-- A special case of `pi.algebra` for when `f = λ i, matrix (m i) (m i) A`. -/
 instance Pi.matrixAlgebra (I R A : Type _) (m : I → Type _) [CommSemiring R] [Semiring A]
     [Algebra R A] [∀ i, Fintype (m i)] [∀ i, DecidableEq (m i)] :
     Algebra R (∀ i, Matrix (m i) (m i) A) :=
   @Pi.algebra I R (fun i => Matrix (m i) (m i) A) _ _ fun i => Matrix.instAlgebra
 #align pi.matrix_algebra Pi.matrixAlgebra
--/
 
-#print Pi.matrix_topologicalRing /-
 /-- A special case of `pi.topological_ring` for when `f = λ i, matrix (m i) (m i) A`. -/
 instance Pi.matrix_topologicalRing (I A : Type _) (m : I → Type _) [Ring A] [TopologicalSpace A]
     [TopologicalRing A] [∀ i, Fintype (m i)] : TopologicalRing (∀ i, Matrix (m i) (m i) A) :=
   @Pi.instTopologicalRing _ (fun i => Matrix (m i) (m i) A) _ _ fun i => Matrix.topologicalRing
 #align pi.matrix_topological_ring Pi.matrix_topologicalRing
--/
 
 end HacksForPiInstanceSearch
 

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

@@ -2,11 +2,6 @@
 Copyright (c) 2022 Eric Wieser. All rights reserved.
 Released under Apache 2.0 license as described in the file LICENSE.
 Authors: Eric Wieser
-
-! This file was ported from Lean 3 source module analysis.normed_space.matrix_exponential
-! leanprover-community/mathlib commit 5d0c76894ada7940957143163d7b921345474cbc
-! Please do not edit these lines, except to modify the commit id
-! if you have ported upstream changes.
 -/
 import Mathbin.Analysis.NormedSpace.Exponential
 import Mathbin.Analysis.Matrix
@@ -15,6 +10,8 @@ import Mathbin.LinearAlgebra.Matrix.Hermitian
 import Mathbin.LinearAlgebra.Matrix.Symmetric
 import Mathbin.Topology.UniformSpace.Matrix
 
+#align_import analysis.normed_space.matrix_exponential from "leanprover-community/mathlib"@"5d0c76894ada7940957143163d7b921345474cbc"
+
 /-!
 # Lemmas about the matrix exponential
 

mathlib commit https://github.com/leanprover-community/mathlib/commit/93f880918cb51905fd51b76add8273cbc27718ab

@@ -4,7 +4,7 @@ Released under Apache 2.0 license as described in the file LICENSE.
 Authors: Eric Wieser
 
 ! This file was ported from Lean 3 source module analysis.normed_space.matrix_exponential
-! leanprover-community/mathlib commit 1e3201306d4d9eb1fd54c60d7c4510ad5126f6f9
+! leanprover-community/mathlib commit 5d0c76894ada7940957143163d7b921345474cbc
 ! Please do not edit these lines, except to modify the commit id
 ! if you have ported upstream changes.
 -/
@@ -18,6 +18,9 @@ import Mathbin.Topology.UniformSpace.Matrix
 /-!
 # Lemmas about the matrix exponential
 
+> THIS FILE IS SYNCHRONIZED WITH MATHLIB4.
+> Any changes to this file require a corresponding PR to mathlib4.
+
 In this file, we provide results about `exp` on `matrix`s over a topological or normed algebra.
 Note that generic results over all topological spaces such as `exp_zero` can be used on matrices
 without issue, so are not repeated here. The topological results specific to matrices are:

mathlib commit https://github.com/leanprover-community/mathlib/commit/6285167a053ad0990fc88e56c48ccd9fae6550eb

@@ -73,30 +73,38 @@ open scoped Matrix BigOperators
 
 section HacksForPiInstanceSearch
 
+#print Function.topologicalRing /-
 /-- A special case of `pi.topological_ring` for when `R` is not dependently typed. -/
 instance Function.topologicalRing (I : Type _) (R : Type _) [NonUnitalRing R] [TopologicalSpace R]
     [TopologicalRing R] : TopologicalRing (I → R) :=
-  Pi.topologicalRing
+  Pi.instTopologicalRing
 #align function.topological_ring Function.topologicalRing
+-/
 
+#print Function.algebraRing /-
 /-- A special case of `function.algebra` for when A is a `ring` not a `semiring` -/
 instance Function.algebraRing (I : Type _) {R : Type _} (A : Type _) [CommSemiring R] [Ring A]
     [Algebra R A] : Algebra R (I → A) :=
   Pi.algebra _ _
 #align function.algebra_ring Function.algebraRing
+-/
 
+#print Pi.matrixAlgebra /-
 /-- A special case of `pi.algebra` for when `f = λ i, matrix (m i) (m i) A`. -/
 instance Pi.matrixAlgebra (I R A : Type _) (m : I → Type _) [CommSemiring R] [Semiring A]
     [Algebra R A] [∀ i, Fintype (m i)] [∀ i, DecidableEq (m i)] :
     Algebra R (∀ i, Matrix (m i) (m i) A) :=
-  @Pi.algebra I R (fun i => Matrix (m i) (m i) A) _ _ fun i => Matrix.algebra
+  @Pi.algebra I R (fun i => Matrix (m i) (m i) A) _ _ fun i => Matrix.instAlgebra
 #align pi.matrix_algebra Pi.matrixAlgebra
+-/
 
+#print Pi.matrix_topologicalRing /-
 /-- A special case of `pi.topological_ring` for when `f = λ i, matrix (m i) (m i) A`. -/
 instance Pi.matrix_topologicalRing (I A : Type _) (m : I → Type _) [Ring A] [TopologicalSpace A]
     [TopologicalRing A] [∀ i, Fintype (m i)] : TopologicalRing (∀ i, Matrix (m i) (m i) A) :=
-  @Pi.topologicalRing _ (fun i => Matrix (m i) (m i) A) _ _ fun i => Matrix.topologicalRing
+  @Pi.instTopologicalRing _ (fun i => Matrix (m i) (m i) A) _ _ fun i => Matrix.topologicalRing
 #align pi.matrix_topological_ring Pi.matrix_topologicalRing
+-/
 
 end HacksForPiInstanceSearch
 
@@ -112,29 +120,39 @@ variable [Fintype m] [DecidableEq m] [Fintype n] [DecidableEq n] [∀ i, Fintype
   [∀ i, DecidableEq (n' i)] [Field 𝕂] [Ring 𝔸] [TopologicalSpace 𝔸] [TopologicalRing 𝔸]
   [Algebra 𝕂 𝔸] [T2Space 𝔸]
 
+#print Matrix.exp_diagonal /-
 theorem exp_diagonal (v : m → 𝔸) : exp 𝕂 (diagonal v) = diagonal (exp 𝕂 v) := by
   simp_rw [exp_eq_tsum, diagonal_pow, ← diagonal_smul, ← diagonal_tsum]
 #align matrix.exp_diagonal Matrix.exp_diagonal
+-/
 
+#print Matrix.exp_blockDiagonal /-
 theorem exp_blockDiagonal (v : m → Matrix n n 𝔸) :
     exp 𝕂 (blockDiagonal v) = blockDiagonal (exp 𝕂 v) := by
   simp_rw [exp_eq_tsum, ← block_diagonal_pow, ← block_diagonal_smul, ← block_diagonal_tsum]
 #align matrix.exp_block_diagonal Matrix.exp_blockDiagonal
+-/
 
+#print Matrix.exp_blockDiagonal' /-
 theorem exp_blockDiagonal' (v : ∀ i, Matrix (n' i) (n' i) 𝔸) :
     exp 𝕂 (blockDiagonal' v) = blockDiagonal' (exp 𝕂 v) := by
   simp_rw [exp_eq_tsum, ← block_diagonal'_pow, ← block_diagonal'_smul, ← block_diagonal'_tsum]
 #align matrix.exp_block_diagonal' Matrix.exp_blockDiagonal'
+-/
 
+#print Matrix.exp_conjTranspose /-
 theorem exp_conjTranspose [StarRing 𝔸] [ContinuousStar 𝔸] (A : Matrix m m 𝔸) :
     exp 𝕂 Aᴴ = (exp 𝕂 A)ᴴ :=
   (star_exp A).symm
 #align matrix.exp_conj_transpose Matrix.exp_conjTranspose
+-/
 
+#print Matrix.IsHermitian.exp /-
 theorem IsHermitian.exp [StarRing 𝔸] [ContinuousStar 𝔸] {A : Matrix m m 𝔸} (h : A.IsHermitian) :
     (exp 𝕂 A).IsHermitian :=
   (exp_conjTranspose _ _).symm.trans <| congr_arg _ h
 #align matrix.is_hermitian.exp Matrix.IsHermitian.exp
+-/
 
 end Ring
 
@@ -143,13 +161,17 @@ section CommRing
 variable [Fintype m] [DecidableEq m] [Field 𝕂] [CommRing 𝔸] [TopologicalSpace 𝔸] [TopologicalRing 𝔸]
   [Algebra 𝕂 𝔸] [T2Space 𝔸]
 
+#print Matrix.exp_transpose /-
 theorem exp_transpose (A : Matrix m m 𝔸) : exp 𝕂 Aᵀ = (exp 𝕂 A)ᵀ := by
   simp_rw [exp_eq_tsum, transpose_tsum, transpose_smul, transpose_pow]
 #align matrix.exp_transpose Matrix.exp_transpose
+-/
 
+#print Matrix.IsSymm.exp /-
 theorem IsSymm.exp {A : Matrix m m 𝔸} (h : A.IsSymm) : (exp 𝕂 A).IsSymm :=
   (exp_transpose _ _).symm.trans <| congr_arg _ h
 #align matrix.is_symm.exp Matrix.IsSymm.exp
+-/
 
 end CommRing
 
@@ -160,6 +182,7 @@ section Normed
 variable [IsROrC 𝕂] [Fintype m] [DecidableEq m] [Fintype n] [DecidableEq n] [∀ i, Fintype (n' i)]
   [∀ i, DecidableEq (n' i)] [NormedRing 𝔸] [NormedAlgebra 𝕂 𝔸] [CompleteSpace 𝔸]
 
+#print Matrix.exp_add_of_commute /-
 theorem exp_add_of_commute (A B : Matrix m m 𝔸) (h : Commute A B) :
     exp 𝕂 (A + B) = exp 𝕂 A ⬝ exp 𝕂 B :=
   by
@@ -168,7 +191,9 @@ theorem exp_add_of_commute (A B : Matrix m m 𝔸) (h : Commute A B) :
   letI : NormedAlgebra 𝕂 (Matrix m m 𝔸) := Matrix.linftyOpNormedAlgebra
   exact exp_add_of_commute h
 #align matrix.exp_add_of_commute Matrix.exp_add_of_commute
+-/
 
+#print Matrix.exp_sum_of_commute /-
 theorem exp_sum_of_commute {ι} (s : Finset ι) (f : ι → Matrix m m 𝔸)
     (h : (s : Set ι).Pairwise fun i j => Commute (f i) (f j)) :
     exp 𝕂 (∑ i in s, f i) =
@@ -179,7 +204,9 @@ theorem exp_sum_of_commute {ι} (s : Finset ι) (f : ι → Matrix m m 𝔸)
   letI : NormedAlgebra 𝕂 (Matrix m m 𝔸) := Matrix.linftyOpNormedAlgebra
   exact exp_sum_of_commute s f h
 #align matrix.exp_sum_of_commute Matrix.exp_sum_of_commute
+-/
 
+#print Matrix.exp_nsmul /-
 theorem exp_nsmul (n : ℕ) (A : Matrix m m 𝔸) : exp 𝕂 (n • A) = exp 𝕂 A ^ n :=
   by
   letI : SeminormedRing (Matrix m m 𝔸) := Matrix.linftyOpSemiNormedRing
@@ -187,7 +214,9 @@ theorem exp_nsmul (n : ℕ) (A : Matrix m m 𝔸) : exp 𝕂 (n • A) = exp 
   letI : NormedAlgebra 𝕂 (Matrix m m 𝔸) := Matrix.linftyOpNormedAlgebra
   exact exp_nsmul n A
 #align matrix.exp_nsmul Matrix.exp_nsmul
+-/
 
+#print Matrix.isUnit_exp /-
 theorem isUnit_exp (A : Matrix m m 𝔸) : IsUnit (exp 𝕂 A) :=
   by
   letI : SeminormedRing (Matrix m m 𝔸) := Matrix.linftyOpSemiNormedRing
@@ -195,7 +224,9 @@ theorem isUnit_exp (A : Matrix m m 𝔸) : IsUnit (exp 𝕂 A) :=
   letI : NormedAlgebra 𝕂 (Matrix m m 𝔸) := Matrix.linftyOpNormedAlgebra
   exact isUnit_exp _ A
 #align matrix.is_unit_exp Matrix.isUnit_exp
+-/
 
+#print Matrix.exp_units_conj /-
 theorem exp_units_conj (U : (Matrix m m 𝔸)ˣ) (A : Matrix m m 𝔸) :
     exp 𝕂 (↑U ⬝ A ⬝ ↑U⁻¹ : Matrix m m 𝔸) = ↑U ⬝ exp 𝕂 A ⬝ ↑U⁻¹ :=
   by
@@ -204,11 +235,14 @@ theorem exp_units_conj (U : (Matrix m m 𝔸)ˣ) (A : Matrix m m 𝔸) :
   letI : NormedAlgebra 𝕂 (Matrix m m 𝔸) := Matrix.linftyOpNormedAlgebra
   exact exp_units_conj _ U A
 #align matrix.exp_units_conj Matrix.exp_units_conj
+-/
 
+#print Matrix.exp_units_conj' /-
 theorem exp_units_conj' (U : (Matrix m m 𝔸)ˣ) (A : Matrix m m 𝔸) :
     exp 𝕂 (↑U⁻¹ ⬝ A ⬝ U : Matrix m m 𝔸) = ↑U⁻¹ ⬝ exp 𝕂 A ⬝ U :=
   exp_units_conj 𝕂 U⁻¹ A
 #align matrix.exp_units_conj' Matrix.exp_units_conj'
+-/
 
 end Normed
 
@@ -217,6 +251,7 @@ section NormedComm
 variable [IsROrC 𝕂] [Fintype m] [DecidableEq m] [Fintype n] [DecidableEq n] [∀ i, Fintype (n' i)]
   [∀ i, DecidableEq (n' i)] [NormedCommRing 𝔸] [NormedAlgebra 𝕂 𝔸] [CompleteSpace 𝔸]
 
+#print Matrix.exp_neg /-
 theorem exp_neg (A : Matrix m m 𝔸) : exp 𝕂 (-A) = (exp 𝕂 A)⁻¹ :=
   by
   rw [nonsing_inv_eq_ring_inverse]
@@ -225,7 +260,9 @@ theorem exp_neg (A : Matrix m m 𝔸) : exp 𝕂 (-A) = (exp 𝕂 A)⁻¹ :=
   letI : NormedAlgebra 𝕂 (Matrix m m 𝔸) := Matrix.linftyOpNormedAlgebra
   exact (Ring.inverse_exp _ A).symm
 #align matrix.exp_neg Matrix.exp_neg
+-/
 
+#print Matrix.exp_zsmul /-
 theorem exp_zsmul (z : ℤ) (A : Matrix m m 𝔸) : exp 𝕂 (z • A) = exp 𝕂 A ^ z :=
   by
   obtain ⟨n, rfl | rfl⟩ := z.eq_coe_or_neg
@@ -233,18 +270,23 @@ theorem exp_zsmul (z : ℤ) (A : Matrix m m 𝔸) : exp 𝕂 (z • A) = exp 
   · have : IsUnit (exp 𝕂 A).det := (Matrix.isUnit_iff_isUnit_det _).mp (isUnit_exp _ _)
     rw [Matrix.zpow_neg this, zpow_ofNat, neg_smul, exp_neg, coe_nat_zsmul, exp_nsmul]
 #align matrix.exp_zsmul Matrix.exp_zsmul
+-/
 
+#print Matrix.exp_conj /-
 theorem exp_conj (U : Matrix m m 𝔸) (A : Matrix m m 𝔸) (hy : IsUnit U) :
     exp 𝕂 (U ⬝ A ⬝ U⁻¹) = U ⬝ exp 𝕂 A ⬝ U⁻¹ :=
   let ⟨u, hu⟩ := hy
   hu ▸ by simpa only [Matrix.coe_units_inv] using exp_units_conj 𝕂 u A
 #align matrix.exp_conj Matrix.exp_conj
+-/
 
+#print Matrix.exp_conj' /-
 theorem exp_conj' (U : Matrix m m 𝔸) (A : Matrix m m 𝔸) (hy : IsUnit U) :
     exp 𝕂 (U⁻¹ ⬝ A ⬝ U) = U⁻¹ ⬝ exp 𝕂 A ⬝ U :=
   let ⟨u, hu⟩ := hy
   hu ▸ by simpa only [Matrix.coe_units_inv] using exp_units_conj' 𝕂 u A
 #align matrix.exp_conj' Matrix.exp_conj'
+-/
 
 end NormedComm
 

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

@@ -69,7 +69,7 @@ Hopefully we will be able to remove these in Lean 4.
 -/
 
 
-open Matrix BigOperators
+open scoped Matrix BigOperators
 
 section HacksForPiInstanceSearch
 

mathlib commit https://github.com/leanprover-community/mathlib/commit/2196ab363eb097c008d4497125e0dde23fb36db2

@@ -4,13 +4,15 @@ Released under Apache 2.0 license as described in the file LICENSE.
 Authors: Eric Wieser
 
 ! This file was ported from Lean 3 source module analysis.normed_space.matrix_exponential
-! leanprover-community/mathlib commit 31263840fccb6bc5ea3d3d49676a1d16d596cfc0
+! leanprover-community/mathlib commit 1e3201306d4d9eb1fd54c60d7c4510ad5126f6f9
 ! Please do not edit these lines, except to modify the commit id
 ! if you have ported upstream changes.
 -/
 import Mathbin.Analysis.NormedSpace.Exponential
 import Mathbin.Analysis.Matrix
 import Mathbin.LinearAlgebra.Matrix.Zpow
+import Mathbin.LinearAlgebra.Matrix.Hermitian
+import Mathbin.LinearAlgebra.Matrix.Symmetric
 import Mathbin.Topology.UniformSpace.Matrix
 
 /-!
@@ -129,6 +131,11 @@ theorem exp_conjTranspose [StarRing 𝔸] [ContinuousStar 𝔸] (A : Matrix m m
   (star_exp A).symm
 #align matrix.exp_conj_transpose Matrix.exp_conjTranspose
 
+theorem IsHermitian.exp [StarRing 𝔸] [ContinuousStar 𝔸] {A : Matrix m m 𝔸} (h : A.IsHermitian) :
+    (exp 𝕂 A).IsHermitian :=
+  (exp_conjTranspose _ _).symm.trans <| congr_arg _ h
+#align matrix.is_hermitian.exp Matrix.IsHermitian.exp
+
 end Ring
 
 section CommRing
@@ -140,6 +147,10 @@ theorem exp_transpose (A : Matrix m m 𝔸) : exp 𝕂 Aᵀ = (exp 𝕂 A)ᵀ :=
   simp_rw [exp_eq_tsum, transpose_tsum, transpose_smul, transpose_pow]
 #align matrix.exp_transpose Matrix.exp_transpose
 
+theorem IsSymm.exp {A : Matrix m m 𝔸} (h : A.IsSymm) : (exp 𝕂 A).IsSymm :=
+  (exp_transpose _ _).symm.trans <| congr_arg _ h
+#align matrix.is_symm.exp Matrix.IsSymm.exp
+
 end CommRing
 
 end Topological

mathlib commit https://github.com/leanprover-community/mathlib/commit/2af0836443b4cfb5feda0df0051acdb398304931

@@ -152,7 +152,7 @@ variable [IsROrC 𝕂] [Fintype m] [DecidableEq m] [Fintype n] [DecidableEq n] [
 theorem exp_add_of_commute (A B : Matrix m m 𝔸) (h : Commute A B) :
     exp 𝕂 (A + B) = exp 𝕂 A ⬝ exp 𝕂 B :=
   by
-  letI : SemiNormedRing (Matrix m m 𝔸) := Matrix.linftyOpSemiNormedRing
+  letI : SeminormedRing (Matrix m m 𝔸) := Matrix.linftyOpSemiNormedRing
   letI : NormedRing (Matrix m m 𝔸) := Matrix.linftyOpNormedRing
   letI : NormedAlgebra 𝕂 (Matrix m m 𝔸) := Matrix.linftyOpNormedAlgebra
   exact exp_add_of_commute h
@@ -163,7 +163,7 @@ theorem exp_sum_of_commute {ι} (s : Finset ι) (f : ι → Matrix m m 𝔸)
     exp 𝕂 (∑ i in s, f i) =
       s.noncommProd (fun i => exp 𝕂 (f i)) fun i hi j hj _ => (h.of_refl hi hj).exp 𝕂 :=
   by
-  letI : SemiNormedRing (Matrix m m 𝔸) := Matrix.linftyOpSemiNormedRing
+  letI : SeminormedRing (Matrix m m 𝔸) := Matrix.linftyOpSemiNormedRing
   letI : NormedRing (Matrix m m 𝔸) := Matrix.linftyOpNormedRing
   letI : NormedAlgebra 𝕂 (Matrix m m 𝔸) := Matrix.linftyOpNormedAlgebra
   exact exp_sum_of_commute s f h
@@ -171,7 +171,7 @@ theorem exp_sum_of_commute {ι} (s : Finset ι) (f : ι → Matrix m m 𝔸)
 
 theorem exp_nsmul (n : ℕ) (A : Matrix m m 𝔸) : exp 𝕂 (n • A) = exp 𝕂 A ^ n :=
   by
-  letI : SemiNormedRing (Matrix m m 𝔸) := Matrix.linftyOpSemiNormedRing
+  letI : SeminormedRing (Matrix m m 𝔸) := Matrix.linftyOpSemiNormedRing
   letI : NormedRing (Matrix m m 𝔸) := Matrix.linftyOpNormedRing
   letI : NormedAlgebra 𝕂 (Matrix m m 𝔸) := Matrix.linftyOpNormedAlgebra
   exact exp_nsmul n A
@@ -179,7 +179,7 @@ theorem exp_nsmul (n : ℕ) (A : Matrix m m 𝔸) : exp 𝕂 (n • A) = exp 
 
 theorem isUnit_exp (A : Matrix m m 𝔸) : IsUnit (exp 𝕂 A) :=
   by
-  letI : SemiNormedRing (Matrix m m 𝔸) := Matrix.linftyOpSemiNormedRing
+  letI : SeminormedRing (Matrix m m 𝔸) := Matrix.linftyOpSemiNormedRing
   letI : NormedRing (Matrix m m 𝔸) := Matrix.linftyOpNormedRing
   letI : NormedAlgebra 𝕂 (Matrix m m 𝔸) := Matrix.linftyOpNormedAlgebra
   exact isUnit_exp _ A
@@ -188,7 +188,7 @@ theorem isUnit_exp (A : Matrix m m 𝔸) : IsUnit (exp 𝕂 A) :=
 theorem exp_units_conj (U : (Matrix m m 𝔸)ˣ) (A : Matrix m m 𝔸) :
     exp 𝕂 (↑U ⬝ A ⬝ ↑U⁻¹ : Matrix m m 𝔸) = ↑U ⬝ exp 𝕂 A ⬝ ↑U⁻¹ :=
   by
-  letI : SemiNormedRing (Matrix m m 𝔸) := Matrix.linftyOpSemiNormedRing
+  letI : SeminormedRing (Matrix m m 𝔸) := Matrix.linftyOpSemiNormedRing
   letI : NormedRing (Matrix m m 𝔸) := Matrix.linftyOpNormedRing
   letI : NormedAlgebra 𝕂 (Matrix m m 𝔸) := Matrix.linftyOpNormedAlgebra
   exact exp_units_conj _ U A
@@ -209,7 +209,7 @@ variable [IsROrC 𝕂] [Fintype m] [DecidableEq m] [Fintype n] [DecidableEq n] [
 theorem exp_neg (A : Matrix m m 𝔸) : exp 𝕂 (-A) = (exp 𝕂 A)⁻¹ :=
   by
   rw [nonsing_inv_eq_ring_inverse]
-  letI : SemiNormedRing (Matrix m m 𝔸) := Matrix.linftyOpSemiNormedRing
+  letI : SeminormedRing (Matrix m m 𝔸) := Matrix.linftyOpSemiNormedRing
   letI : NormedRing (Matrix m m 𝔸) := Matrix.linftyOpNormedRing
   letI : NormedAlgebra 𝕂 (Matrix m m 𝔸) := Matrix.linftyOpNormedAlgebra
   exact (Ring.inverse_exp _ A).symm

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

This is less exhaustive than its sibling #11486 because edge cases are harder to classify. No fundamental difficulty, just me being a bit fast and lazy.

Reduce the diff of #11203

@@ -189,9 +189,9 @@ theorem exp_neg (A : Matrix m m 𝔸) : exp 𝕂 (-A) = (exp 𝕂 A)⁻¹ := by
 
 theorem exp_zsmul (z : ℤ) (A : Matrix m m 𝔸) : exp 𝕂 (z • A) = exp 𝕂 A ^ z := by
   obtain ⟨n, rfl | rfl⟩ := z.eq_nat_or_neg
-  · rw [zpow_coe_nat, natCast_zsmul, exp_nsmul]
+  · rw [zpow_natCast, natCast_zsmul, exp_nsmul]
   · have : IsUnit (exp 𝕂 A).det := (Matrix.isUnit_iff_isUnit_det _).mp (isUnit_exp _ _)
-    rw [Matrix.zpow_neg this, zpow_coe_nat, neg_smul, exp_neg, natCast_zsmul, exp_nsmul]
+    rw [Matrix.zpow_neg this, zpow_natCast, neg_smul, exp_neg, natCast_zsmul, exp_nsmul]
 #align matrix.exp_zsmul Matrix.exp_zsmul
 
 theorem exp_conj (U : Matrix m m 𝔸) (A : Matrix m m 𝔸) (hy : IsUnit U) :

@@ -16,8 +16,9 @@ import Mathlib.Topology.UniformSpace.Matrix
 # Lemmas about the matrix exponential
 
 In this file, we provide results about `exp` on `Matrix`s over a topological or normed algebra.
-Note that generic results over all topological spaces such as `exp_zero` can be used on matrices
-without issue, so are not repeated here. The topological results specific to matrices are:
+Note that generic results over all topological spaces such as `NormedSpace.exp_zero`
+can be used on matrices without issue, so are not repeated here.
+The topological results specific to matrices are:
 
 * `Matrix.exp_transpose`
 * `Matrix.exp_conjTranspose`
@@ -25,15 +26,15 @@ without issue, so are not repeated here. The topological results specific to mat
 * `Matrix.exp_blockDiagonal`
 * `Matrix.exp_blockDiagonal'`
 
-Lemmas like `exp_add_of_commute` require a canonical norm on the type; while there are multiple
-sensible choices for the norm of a `Matrix` (`Matrix.normedAddCommGroup`,
+Lemmas like `NormedSpace.exp_add_of_commute` require a canonical norm on the type;
+while there are multiple sensible choices for the norm of a `Matrix` (`Matrix.normedAddCommGroup`,
 `Matrix.frobeniusNormedAddCommGroup`, `Matrix.linftyOpNormedAddCommGroup`), none of them
 are canonical. In an application where a particular norm is chosen using
-`attribute [local instance]`, then the usual lemmas about `exp` are fine. When choosing a norm is
-undesirable, the results in this file can be used.
+`attribute [local instance]`, then the usual lemmas about `NormedSpace.exp` are fine.
+When choosing a norm is undesirable, the results in this file can be used.
 
-In this file, we copy across the lemmas about `exp`, but hide the requirement for a norm inside the
-proof.
+In this file, we copy across the lemmas about `NormedSpace.exp`,
+but hide the requirement for a norm inside the proof.
 
 * `Matrix.exp_add_of_commute`
 * `Matrix.exp_sum_of_commute`

IsROrC contains data, which goes against the expectation that classes prefixed with Is are prop-valued. People have been complaining about this on and off, so this PR renames IsROrC to RCLike.

@@ -121,7 +121,7 @@ end Topological
 
 section Normed
 
-variable [IsROrC 𝕂] [Fintype m] [DecidableEq m] [Fintype n] [DecidableEq n] [∀ i, Fintype (n' i)]
+variable [RCLike 𝕂] [Fintype m] [DecidableEq m] [Fintype n] [DecidableEq n] [∀ i, Fintype (n' i)]
   [∀ i, DecidableEq (n' i)] [NormedRing 𝔸] [NormedAlgebra 𝕂 𝔸] [CompleteSpace 𝔸]
 
 nonrec theorem exp_add_of_commute (A B : Matrix m m 𝔸) (h : Commute A B) :
@@ -175,7 +175,7 @@ end Normed
 
 section NormedComm
 
-variable [IsROrC 𝕂] [Fintype m] [DecidableEq m] [Fintype n] [DecidableEq n] [∀ i, Fintype (n' i)]
+variable [RCLike 𝕂] [Fintype m] [DecidableEq m] [Fintype n] [DecidableEq n] [∀ i, Fintype (n' i)]
   [∀ i, DecidableEq (n' i)] [NormedCommRing 𝔸] [NormedAlgebra 𝕂 𝔸] [CompleteSpace 𝔸]
 
 theorem exp_neg (A : Matrix m m 𝔸) : exp 𝕂 (-A) = (exp 𝕂 A)⁻¹ := by

... and add a deprecated alias for the old name. This is mostly just me discovering the power of F2

@@ -188,9 +188,9 @@ theorem exp_neg (A : Matrix m m 𝔸) : exp 𝕂 (-A) = (exp 𝕂 A)⁻¹ := by
 
 theorem exp_zsmul (z : ℤ) (A : Matrix m m 𝔸) : exp 𝕂 (z • A) = exp 𝕂 A ^ z := by
   obtain ⟨n, rfl | rfl⟩ := z.eq_nat_or_neg
-  · rw [zpow_coe_nat, coe_nat_zsmul, exp_nsmul]
+  · rw [zpow_coe_nat, natCast_zsmul, exp_nsmul]
   · have : IsUnit (exp 𝕂 A).det := (Matrix.isUnit_iff_isUnit_det _).mp (isUnit_exp _ _)
-    rw [Matrix.zpow_neg this, zpow_coe_nat, neg_smul, exp_neg, coe_nat_zsmul, exp_nsmul]
+    rw [Matrix.zpow_neg this, zpow_coe_nat, neg_smul, exp_neg, natCast_zsmul, exp_nsmul]
 #align matrix.exp_zsmul Matrix.exp_zsmul
 
 theorem exp_conj (U : Matrix m m 𝔸) (A : Matrix m m 𝔸) (hy : IsUnit U) :

Previously these were syntactically identical to the corresponding zpow_coe_nat and coe_nat_zsmul lemmas, now they are about OfNat.ofNat.

Unfortunately, almost every call site uses the ofNat name to refer to Nat.cast, so the downstream proofs had to be adjusted too.

@@ -188,9 +188,9 @@ theorem exp_neg (A : Matrix m m 𝔸) : exp 𝕂 (-A) = (exp 𝕂 A)⁻¹ := by
 
 theorem exp_zsmul (z : ℤ) (A : Matrix m m 𝔸) : exp 𝕂 (z • A) = exp 𝕂 A ^ z := by
   obtain ⟨n, rfl | rfl⟩ := z.eq_nat_or_neg
-  · rw [zpow_ofNat, coe_nat_zsmul, exp_nsmul]
+  · rw [zpow_coe_nat, coe_nat_zsmul, exp_nsmul]
   · have : IsUnit (exp 𝕂 A).det := (Matrix.isUnit_iff_isUnit_det _).mp (isUnit_exp _ _)
-    rw [Matrix.zpow_neg this, zpow_ofNat, neg_smul, exp_neg, coe_nat_zsmul, exp_nsmul]
+    rw [Matrix.zpow_neg this, zpow_coe_nat, neg_smul, exp_neg, coe_nat_zsmul, exp_nsmul]
 #align matrix.exp_zsmul Matrix.exp_zsmul
 
 theorem exp_conj (U : Matrix m m 𝔸) (A : Matrix m m 𝔸) (hy : IsUnit U) :

@@ -29,7 +29,7 @@ Lemmas like `exp_add_of_commute` require a canonical norm on the type; while the
 sensible choices for the norm of a `Matrix` (`Matrix.normedAddCommGroup`,
 `Matrix.frobeniusNormedAddCommGroup`, `Matrix.linftyOpNormedAddCommGroup`), none of them
 are canonical. In an application where a particular norm is chosen using
-`local attribute [instance]`, then the usual lemmas about `exp` are fine. When choosing a norm is
+`attribute [local instance]`, then the usual lemmas about `exp` are fine. When choosing a norm is
 undesirable, the results in this file can be used.
 
 In this file, we copy across the lemmas about `exp`, but hide the requirement for a norm inside the

Per discussion at zulip

Co-authored-by: Scott Morrison <scott.morrison@gmail.com>

@@ -62,6 +62,8 @@ results for general rings are instead stated about `Ring.inverse`:
 
 open scoped Matrix BigOperators
 
+open NormedSpace -- For `exp`.
+
 variable (𝕂 : Type*) {m n p : Type*} {n' : m → Type*} {𝔸 : Type*}
 
 namespace Matrix

The file still compiles without these, so I guess as predicted we no longer need them. They were certainly needed in Lean 3.

@@ -50,12 +50,6 @@ results for general rings are instead stated about `Ring.inverse`:
 * `Matrix.exp_conj`
 * `Matrix.exp_conj'`
 
-## Implementation notes
-
-This file runs into some sharp edges on typeclass search in lean 3, especially regarding pi types.
-To work around this, we copy a handful of instances for when lean can't find them by itself.
-Hopefully we will be able to remove these in Lean 4.
-
 ## TODO
 
 * Show that `Matrix.det (exp 𝕂 A) = exp 𝕂 (Matrix.trace A)`
@@ -68,35 +62,6 @@ Hopefully we will be able to remove these in Lean 4.
 
 open scoped Matrix BigOperators
 
-section HacksForPiInstanceSearch
-
-/-- A special case of `Pi.instTopologicalRing` for when `R` is not dependently typed. -/
-instance Function.topologicalRing (I : Type*) (R : Type*) [NonUnitalRing R] [TopologicalSpace R]
-    [TopologicalRing R] : TopologicalRing (I → R) :=
-  Pi.instTopologicalRing
-#align function.topological_ring Function.topologicalRing
-
-/-- A special case of `Function.algebra` for when A is a `Ring` not a `Semiring` -/
-instance Function.algebraRing (I : Type*) {R : Type*} (A : Type*) [CommSemiring R] [Ring A]
-    [Algebra R A] : Algebra R (I → A) :=
-  Pi.algebra _ _
-#align function.algebra_ring Function.algebraRing
-
-/-- A special case of `Pi.algebra` for when `f = λ i, Matrix (m i) (m i) A`. -/
-instance Pi.matrixAlgebra (I R A : Type*) (m : I → Type*) [CommSemiring R] [Semiring A]
-    [Algebra R A] [∀ i, Fintype (m i)] [∀ i, DecidableEq (m i)] :
-    Algebra R (∀ i, Matrix (m i) (m i) A) :=
-  @Pi.algebra I R (fun i => Matrix (m i) (m i) A) _ _ fun _ => Matrix.instAlgebra
-#align pi.matrix_algebra Pi.matrixAlgebra
-
-/-- A special case of `Pi.instTopologicalRing` for when `f = λ i, Matrix (m i) (m i) A`. -/
-instance Pi.matrix_topologicalRing (I A : Type*) (m : I → Type*) [Ring A] [TopologicalSpace A]
-    [TopologicalRing A] [∀ i, Fintype (m i)] : TopologicalRing (∀ i, Matrix (m i) (m i) A) :=
-  @Pi.instTopologicalRing _ (fun i => Matrix (m i) (m i) A) _ _ fun _ => Matrix.topologicalRing
-#align pi.matrix_topological_ring Pi.matrix_topologicalRing
-
-end HacksForPiInstanceSearch
-
 variable (𝕂 : Type*) {m n p : Type*} {n' : m → Type*} {𝔸 : Type*}
 
 namespace Matrix

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).

@@ -158,7 +158,7 @@ variable [IsROrC 𝕂] [Fintype m] [DecidableEq m] [Fintype n] [DecidableEq n] [
   [∀ i, DecidableEq (n' i)] [NormedRing 𝔸] [NormedAlgebra 𝕂 𝔸] [CompleteSpace 𝔸]
 
 nonrec theorem exp_add_of_commute (A B : Matrix m m 𝔸) (h : Commute A B) :
-    exp 𝕂 (A + B) = exp 𝕂 A ⬝ exp 𝕂 B := by
+    exp 𝕂 (A + B) = exp 𝕂 A * exp 𝕂 B := by
   letI : SeminormedRing (Matrix m m 𝔸) := Matrix.linftyOpSemiNormedRing
   letI : NormedRing (Matrix m m 𝔸) := Matrix.linftyOpNormedRing
   letI : NormedAlgebra 𝕂 (Matrix m m 𝔸) := Matrix.linftyOpNormedAlgebra
@@ -189,16 +189,18 @@ nonrec theorem isUnit_exp (A : Matrix m m 𝔸) : IsUnit (exp 𝕂 A) := by
   exact isUnit_exp _ A
 #align matrix.is_unit_exp Matrix.isUnit_exp
 
+-- TODO(mathlib4#6607): fix elaboration so `val` isn't needed
 nonrec theorem exp_units_conj (U : (Matrix m m 𝔸)ˣ) (A : Matrix m m 𝔸) :
-    exp 𝕂 (↑U ⬝ A ⬝ ↑U⁻¹ : Matrix m m 𝔸) = ↑U ⬝ exp 𝕂 A ⬝ ↑U⁻¹ := by
+    exp 𝕂 (U.val * A * (U⁻¹).val) = U.val * exp 𝕂 A * (U⁻¹).val := by
   letI : SeminormedRing (Matrix m m 𝔸) := Matrix.linftyOpSemiNormedRing
   letI : NormedRing (Matrix m m 𝔸) := Matrix.linftyOpNormedRing
   letI : NormedAlgebra 𝕂 (Matrix m m 𝔸) := Matrix.linftyOpNormedAlgebra
   exact exp_units_conj _ U A
 #align matrix.exp_units_conj Matrix.exp_units_conj
 
+-- TODO(mathlib4#6607): fix elaboration so `val` isn't needed
 theorem exp_units_conj' (U : (Matrix m m 𝔸)ˣ) (A : Matrix m m 𝔸) :
-    exp 𝕂 (↑U⁻¹ ⬝ A ⬝ U : Matrix m m 𝔸) = ↑U⁻¹ ⬝ exp 𝕂 A ⬝ U :=
+    exp 𝕂 ((U⁻¹).val * A * U.val) = (U⁻¹).val * exp 𝕂 A * U.val :=
   exp_units_conj 𝕂 U⁻¹ A
 #align matrix.exp_units_conj' Matrix.exp_units_conj'
 
@@ -225,13 +227,13 @@ theorem exp_zsmul (z : ℤ) (A : Matrix m m 𝔸) : exp 𝕂 (z • A) = exp 
 #align matrix.exp_zsmul Matrix.exp_zsmul
 
 theorem exp_conj (U : Matrix m m 𝔸) (A : Matrix m m 𝔸) (hy : IsUnit U) :
-    exp 𝕂 (U ⬝ A ⬝ U⁻¹) = U ⬝ exp 𝕂 A ⬝ U⁻¹ :=
+    exp 𝕂 (U * A * U⁻¹) = U * exp 𝕂 A * U⁻¹ :=
   let ⟨u, hu⟩ := hy
   hu ▸ by simpa only [Matrix.coe_units_inv] using exp_units_conj 𝕂 u A
 #align matrix.exp_conj Matrix.exp_conj
 
 theorem exp_conj' (U : Matrix m m 𝔸) (A : Matrix m m 𝔸) (hy : IsUnit U) :
-    exp 𝕂 (U⁻¹ ⬝ A ⬝ U) = U⁻¹ ⬝ exp 𝕂 A ⬝ U :=
+    exp 𝕂 (U⁻¹ * A * U) = U⁻¹ * exp 𝕂 A * U :=
   let ⟨u, hu⟩ := hy
   hu ▸ by simpa only [Matrix.coe_units_inv] using exp_units_conj' 𝕂 u A
 #align matrix.exp_conj' Matrix.exp_conj'

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

This has nice performance benefits.

@@ -71,33 +71,33 @@ open scoped Matrix BigOperators
 section HacksForPiInstanceSearch
 
 /-- A special case of `Pi.instTopologicalRing` for when `R` is not dependently typed. -/
-instance Function.topologicalRing (I : Type _) (R : Type _) [NonUnitalRing R] [TopologicalSpace R]
+instance Function.topologicalRing (I : Type*) (R : Type*) [NonUnitalRing R] [TopologicalSpace R]
     [TopologicalRing R] : TopologicalRing (I → R) :=
   Pi.instTopologicalRing
 #align function.topological_ring Function.topologicalRing
 
 /-- A special case of `Function.algebra` for when A is a `Ring` not a `Semiring` -/
-instance Function.algebraRing (I : Type _) {R : Type _} (A : Type _) [CommSemiring R] [Ring A]
+instance Function.algebraRing (I : Type*) {R : Type*} (A : Type*) [CommSemiring R] [Ring A]
     [Algebra R A] : Algebra R (I → A) :=
   Pi.algebra _ _
 #align function.algebra_ring Function.algebraRing
 
 /-- A special case of `Pi.algebra` for when `f = λ i, Matrix (m i) (m i) A`. -/
-instance Pi.matrixAlgebra (I R A : Type _) (m : I → Type _) [CommSemiring R] [Semiring A]
+instance Pi.matrixAlgebra (I R A : Type*) (m : I → Type*) [CommSemiring R] [Semiring A]
     [Algebra R A] [∀ i, Fintype (m i)] [∀ i, DecidableEq (m i)] :
     Algebra R (∀ i, Matrix (m i) (m i) A) :=
   @Pi.algebra I R (fun i => Matrix (m i) (m i) A) _ _ fun _ => Matrix.instAlgebra
 #align pi.matrix_algebra Pi.matrixAlgebra
 
 /-- A special case of `Pi.instTopologicalRing` for when `f = λ i, Matrix (m i) (m i) A`. -/
-instance Pi.matrix_topologicalRing (I A : Type _) (m : I → Type _) [Ring A] [TopologicalSpace A]
+instance Pi.matrix_topologicalRing (I A : Type*) (m : I → Type*) [Ring A] [TopologicalSpace A]
     [TopologicalRing A] [∀ i, Fintype (m i)] : TopologicalRing (∀ i, Matrix (m i) (m i) A) :=
   @Pi.instTopologicalRing _ (fun i => Matrix (m i) (m i) A) _ _ fun _ => Matrix.topologicalRing
 #align pi.matrix_topological_ring Pi.matrix_topologicalRing
 
 end HacksForPiInstanceSearch
 
-variable (𝕂 : Type _) {m n p : Type _} {n' : m → Type _} {𝔸 : Type _}
+variable (𝕂 : Type*) {m n p : Type*} {n' : m → Type*} {𝔸 : Type*}
 
 namespace Matrix
 

• depends on: #5966

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

@@ -2,11 +2,6 @@
 Copyright (c) 2022 Eric Wieser. All rights reserved.
 Released under Apache 2.0 license as described in the file LICENSE.
 Authors: Eric Wieser
-
-! This file was ported from Lean 3 source module analysis.normed_space.matrix_exponential
-! leanprover-community/mathlib commit 1e3201306d4d9eb1fd54c60d7c4510ad5126f6f9
-! Please do not edit these lines, except to modify the commit id
-! if you have ported upstream changes.
 -/
 import Mathlib.Analysis.NormedSpace.Exponential
 import Mathlib.Analysis.Matrix
@@ -15,6 +10,8 @@ import Mathlib.LinearAlgebra.Matrix.Hermitian
 import Mathlib.LinearAlgebra.Matrix.Symmetric
 import Mathlib.Topology.UniformSpace.Matrix
 
+#align_import analysis.normed_space.matrix_exponential from "leanprover-community/mathlib"@"1e3201306d4d9eb1fd54c60d7c4510ad5126f6f9"
+
 /-!
 # Lemmas about the matrix exponential