Theorems · Theorem · linear algebra

Matrix.vecMul_injective_iff

∀ {R : Type u_1} [inst : Semiring R] {m : Type u_3} {n : Type u_4} [inst_1 : Fintype m] {M : Matrix m n R},
  (Function.Injective fun v => Matrix.vecMul v M) ↔ LinearIndependent R M.row

Defined in

Mathlib.LinearAlgebra.Matrix.ToLin

Cited by

4 results in Mathlib

Foundations

Depth 82 from the axioms · uses propext, Classical.choice, Quot.sound

Assumes

SemiringFintype