Theorems · Theorem · combinatorics

Matrix.IsHadamard.reindex

∀ {m : Type u_1} {n : Type u_2} {R : Type u_3} [inst : Fintype m] [inst_1 : Fintype n] [inst_2 : DecidableEq m]
  [inst_3 : DecidableEq n] [inst_4 : Semiring R] [inst_5 : StarRing R] {A : Matrix n n R} (e₁ e₂ : n ≃ m),
  A.IsHadamard → ((Matrix.reindex e₁ e₂) A).IsHadamard

Permuting the rows and columns of a Hadamard matrix gives a Hadamard matrix.

Defined in

Mathlib.LinearAlgebra.Matrix.HadamardMatrix

Cited by

1 results in Mathlib

Foundations

Depth 62 from the axioms · uses propext, Classical.choice, Quot.sound

Assumes

FintypeFintypeDecidableEqDecidableEqSemiringStarRing