Theorems · Theorem · linear algebra

Matrix.isAddUnit_detp_mul_detp

∀ {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 * Matrix.detp (-1) B + Matrix.detp (-1) A * Matrix.detp 1 B)

Defined in

Mathlib.LinearAlgebra.Matrix.SemiringInverse

Cited by

1 results in Mathlib

Foundations

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

Assumes

FintypeDecidableEqCommSemiring