Theorems · Theorem · linear algebra

Matrix.det_mul_aux

∀ {n : Type u_2} [inst : DecidableEq n] [inst_1 : Fintype n] {R : Type v} [inst_2 : CommRing R] {M N : Matrix n n R}
  {p : n → n}, ¬Function.Bijective p → ∑ σ, ↑↑(Equiv.Perm.sign σ) * ∏ x, M (σ x) (p x) * N (p x) x = 0

Defined in

Mathlib.LinearAlgebra.Matrix.Determinant.Basic

Cited by

1 results in Mathlib

Foundations

Depth 81 from the axioms · uses propext, Classical.choice, Quot.sound

Assumes

DecidableEqFintypeCommRing