Theorems · Theorem · linear algebra

Matrix.IsDetpBalanced.mul_add_mul_eq

∀ {n : Type u_1} {R : Type u_3} [inst : Fintype n] [inst_1 : DecidableEq n] [inst_2 : CommSemiring R] {A : Matrix n n R}
  {a b : R},
  A.IsDetpBalanced a b →
    ∀ (s t : ℤˣ), a * Matrix.detp s A + b * Matrix.detp t A = b * Matrix.detp s A + a * Matrix.detp t A

Defined in

Mathlib.LinearAlgebra.Matrix.SemiringInverse

Cited by

2 results in Mathlib

Foundations

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

Assumes

FintypeDecidableEqCommSemiring