Theorems · Theorem · linear algebra

Matrix.isAddUnit_detp_smul_mul_adjp

∀ {n : Type u_1} {R : Type u_3} [inst : Fintype n] [inst_1 : DecidableEq n] [inst_2 : CommSemiring R]
  {A B : Matrix n n R} {d : n → R},
  A * B = Matrix.diagonal d →
    IsAddUnit (Matrix.detp 1 A • (B * Matrix.adjp (-1) B) + Matrix.detp (-1) A • (B * Matrix.adjp 1 B))

Defined in

Mathlib.LinearAlgebra.Matrix.SemiringInverse

Cited by

0 results in Mathlib

Foundations

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

Assumes

FintypeDecidableEqCommSemiring