Theorems · Theorem · linear algebra

Matrix.vecMul_surjective_iff_exists_left_inverse

∀ {m : Type u} {n : Type u'} {R : Type u_2} [inst : Semiring R] [inst_1 : DecidableEq n] [inst_2 : Fintype m] [Finite n]
  {A : Matrix m n R}, (Function.Surjective fun v => Matrix.vecMul v A) ↔ ∃ B, B * A = 1

Defined in

Mathlib.LinearAlgebra.Matrix.NonsingularInverse

Cited by

1 results in Mathlib

Foundations

Depth 79 from the axioms · uses propext, Classical.choice, Quot.sound

Assumes

SemiringDecidableEqFintypeFinite