Theorems · Theorem · linear algebra

Matrix.adjugate_mul_distrib

∀ {n : Type v} {α : Type w} [inst : DecidableEq n] [inst_1 : Fintype n] [inst_2 : CommRing α] (A B : Matrix n n α),
  (A * B).adjugate = B.adjugate * A.adjugate

Proof follows from "The trace Cayley-Hamilton theorem" by Darij Grinberg, Section 5.3

Defined in

Mathlib.LinearAlgebra.Matrix.Adjugate

Cited by

3 results in Mathlib

Foundations

Depth 111 from the axioms · uses propext, Classical.choice, Quot.sound

Assumes

DecidableEqFintypeCommRing