File: Mathlib/Analysis/NormedSpace/MatrixExponential.lean

full_name: Matrix.exp_diagonal
code: theorem exp_diagonal (v : m → 𝔸) : exp 𝕂 (diagonal v) = diagonal (exp 𝕂 v) 
goal: NormedSpace.exp 𝕂 (Matrix.diagonal v) = Matrix.diagonal (NormedSpace.exp 𝕂 v)

full_name: Matrix.exp_blockDiagonal
code: theorem exp_blockDiagonal (v : m → Matrix n n 𝔸) :
    exp 𝕂 (blockDiagonal v) = blockDiagonal (exp 𝕂 v) 
goal: NormedSpace.exp 𝕂 (Matrix.blockDiagonal v) = Matrix.blockDiagonal (NormedSpace.exp 𝕂 v)

full_name: Matrix.exp_blockDiagonal'
code: theorem exp_blockDiagonal' (v : ∀ i, Matrix (n' i) (n' i) 𝔸) :
    exp 𝕂 (blockDiagonal' v) = blockDiagonal' (exp 𝕂 v) 
goal: NormedSpace.exp 𝕂 (Matrix.blockDiagonal' v) = Matrix.blockDiagonal' (NormedSpace.exp 𝕂 v)

full_name: Matrix.exp_conjTranspose
code: theorem exp_conjTranspose [StarRing 𝔸] [ContinuousStar 𝔸] (A : Matrix m m 𝔸) :
    exp 𝕂 Aᴴ = (exp 𝕂 A)ᴴ 
goal: NormedSpace.exp 𝕂 Aᴴ = (NormedSpace.exp 𝕂 A)ᴴ

full_name: Matrix.IsHermitian.exp
code: theorem IsHermitian.exp [StarRing 𝔸] [ContinuousStar 𝔸] {A : Matrix m m 𝔸} (h : A.IsHermitian) :
    (exp 𝕂 A).IsHermitian 
goal: (NormedSpace.exp 𝕂 A).IsHermitian

full_name: Matrix.exp_transpose
code: theorem exp_transpose (A : Matrix m m 𝔸) : exp 𝕂 Aᵀ = (exp 𝕂 A)ᵀ 
goal: NormedSpace.exp 𝕂 Aᵀ = (NormedSpace.exp 𝕂 A)ᵀ

full_name: Matrix.IsSymm.exp
code: theorem IsSymm.exp {A : Matrix m m 𝔸} (h : A.IsSymm) : (exp 𝕂 A).IsSymm 
goal: (NormedSpace.exp 𝕂 A).IsSymm

full_name: Matrix.exp_add_of_commute
code: 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 
goal: NormedSpace.exp 𝕂 (A + B) = NormedSpace.exp 𝕂 A * NormedSpace.exp 𝕂 B

full_name: Matrix.exp_sum_of_commute
code: nonrec 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 ∈ s, f i) =
      s.noncommProd (fun i => exp 𝕂 (f i)) fun i hi j hj _ => (h.of_refl hi hj).exp 𝕂 
goal: NormedSpace.exp 𝕂 (∑ i ∈ s, f i) = s.noncommProd (fun i => NormedSpace.exp 𝕂 (f i)) ⋯

full_name: Matrix.exp_nsmul
code: nonrec theorem exp_nsmul (n : ℕ) (A : Matrix m m 𝔸) : exp 𝕂 (n • A) = exp 𝕂 A ^ n 
goal: NormedSpace.exp 𝕂 (n • A) = NormedSpace.exp 𝕂 A ^ n

full_name: Matrix.isUnit_exp
code: nonrec theorem isUnit_exp (A : Matrix m m 𝔸) : IsUnit (exp 𝕂 A) 
goal: IsUnit (NormedSpace.exp 𝕂 A)

full_name: Matrix.exp_units_conj
code: nonrec theorem exp_units_conj (U : (Matrix m m 𝔸)ˣ) (A : Matrix m m 𝔸) :
    exp 𝕂 (U.val * A * (U⁻¹).val) = U.val * exp 𝕂 A * (U⁻¹).val 
goal: NormedSpace.exp 𝕂 (↑U * A * ↑U⁻¹) = ↑U * NormedSpace.exp 𝕂 A * ↑U⁻¹

full_name: Matrix.exp_units_conj'
code: theorem exp_units_conj' (U : (Matrix m m 𝔸)ˣ) (A : Matrix m m 𝔸) :
    exp 𝕂 ((U⁻¹).val * A * U.val) = (U⁻¹).val * exp 𝕂 A * U.val 
goal: NormedSpace.exp 𝕂 (↑U⁻¹ * A * ↑U) = ↑U⁻¹ * NormedSpace.exp 𝕂 A * ↑U

full_name: Matrix.exp_neg
code: theorem exp_neg (A : Matrix m m 𝔸) : exp 𝕂 (-A) = (exp 𝕂 A)⁻¹ 
goal: NormedSpace.exp 𝕂 (-A) = (NormedSpace.exp 𝕂 A)⁻¹

full_name: Matrix.exp_zsmul
code: theorem exp_zsmul (z : ℤ) (A : Matrix m m 𝔸) : exp 𝕂 (z • A) = exp 𝕂 A ^ z 
goal: NormedSpace.exp 𝕂 (z • A) = NormedSpace.exp 𝕂 A ^ z

full_name: Matrix.exp_conj
code: 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 
goal: NormedSpace.exp 𝕂 (U * A * U⁻¹) = U * NormedSpace.exp 𝕂 A * U⁻¹

full_name: Matrix.exp_conj'
code: 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 
goal: NormedSpace.exp 𝕂 (U⁻¹ * A * U) = U⁻¹ * NormedSpace.exp 𝕂 A * U