Theorems · Theorem · combinatorics

Matrix.IsHadamard.det_mul_star_det

∀ {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}, A.IsHadamard → A.det * star A.det = ↑(Fintype.card n) ^ Fintype.card n

The Hadamard determinant identity: det A * star (det A) = (card n)^(card n).

Defined in

Mathlib.LinearAlgebra.Matrix.HadamardMatrix

Cited by

3 results in Mathlib

Foundations

Depth 91 from the axioms · uses propext, Classical.choice, Quot.sound

Assumes

FintypeDecidableEqCommRingStarRing