Theorems · Theorem · combinatorics

Matrix.IsHadamard.transpose

∀ {n : Type u_2} {R : Type u_3} [inst : Fintype n] [inst_1 : DecidableEq n] [inst_2 : CommSemiring R]
  [inst_3 : StarRing R] {A : Matrix n n R}, A.IsHadamard → A.transpose.IsHadamard

The transpose of a Hadamard matrix is Hadamard. Unlike IsHadamard.conjTranspose this requires commutativity: over a noncommutative ring the transpose of a Hadamard matrix need not be Hadamard.

Defined in

Mathlib.LinearAlgebra.Matrix.HadamardMatrix

Cited by

1 results in Mathlib

Foundations

Depth 58 from the axioms · uses propext, Classical.choice, Quot.sound

Assumes

FintypeDecidableEqCommSemiringStarRing