diag_conjTranspose — Mathlib

English

A circulant matrix generated by a constant on the first column equals the scalar (diagonal) matrix with that constant on the diagonal: circulant(Pi.single 0 a) = scalar n a.

Русский

Циркулянтная матрица, порожденная константой на первом столбце, равна скалярной матрице: circulant(Pi.single 0 a) = a I_n.

LaTeX

$$$\\operatorname{circulant}(\\Pi\\text{single }0\\ a) = \\operatorname{scalar}(n)\\,a = a I_n$$$

Lean4

@[simp]
theorem diag_conjTranspose [Star α] (A : Matrix n n α) : diag Aᴴ = star (diag A) :=
  rfl

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