Theorems · Theorem · combinatorics

Matrix.isHadamard_iff_mul_conjTranspose

∀ {n : Type u_2} {R : Type u_3} [inst : Fintype n] [inst_1 : DecidableEq n] [inst_2 : CommRing R] [inst_3 : StarRing R]
  {A : Matrix n n R},
  IsRegular ↑(Fintype.card n) →
    (A.IsHadamard ↔ (∀ (i j : n), A i j ∈ unitary R) ∧ A * A.conjTranspose = ↑(Fintype.card n) • 1)

Defined in

Mathlib.LinearAlgebra.Matrix.HadamardMatrix

Cited by

0 results in Mathlib

Foundations

Depth 101 from the axioms · uses propext, Classical.choice, Quot.sound

Assumes

FintypeDecidableEqCommRingStarRing