conjTranspose_submatrix — Mathlib

English

Conjugate transpose commutes with taking submatrices: (A.submatrix r c)^* = A^* .submatrix c r.

Русский

Сопряжённое транспонирование commute с выборкой подматриц: (A.submatrix r c)^* = A^* .submatrix c r.

LaTeX

$$$(A.submatrix r c)^{*} = A^{*}.submatrix c r$$

Lean4

@[simp]
theorem conjTranspose_submatrix [Star α] (A : Matrix m n α) (r : l → m) (c : o → n) :
    (A.submatrix r c)ᴴ = Aᴴ.submatrix c r :=
  ext fun _ _ => rfl

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