exp — Mathlib

English

For a matrix A over a star-ring with continuous star, exp(A^H) = (exp(A))^H where A^H is the conjugate transpose.

Русский

Если у матрицы A задано сопряжённоеording, то экспонента удовлетворяет exp(A^H) = (exp(A))^H.

LaTeX

$$$\\exp(A^{\\dagger}) = (\\exp(A))^{\\dagger}$$$

Lean4

theorem exp [StarRing 𝔸] [ContinuousStar 𝔸] {A : Matrix m m 𝔸} (h : A.IsHermitian) : (exp 𝕂 A).IsHermitian :=
  (exp_conjTranspose _ _).symm.trans <| congr_arg _ h

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