Theorems · Theorem · linear algebra

LinearIndependent.sum_smul_of_nondegenerate

∀ {ι : Type u_1} {κ : Type u_2} {R : Type u_3} {M : Type u_4} [inst : Fintype ι] [inst_1 : Finite κ]
  [inst_2 : CommRing R] [inst_3 : AddCommGroup M] [inst_4 : Module R M] {v : ι → M},
  LinearIndependent R v → ∀ {A : Matrix κ ι R}, A.Nondegenerate → LinearIndependent R fun i => ∑ j, A i j • v j

Defined in

Mathlib.LinearAlgebra.Matrix.Nondegenerate

Cited by

1 results in Mathlib

Foundations

Depth 84 from the axioms · uses propext, Classical.choice, Quot.sound

Assumes

FintypeFiniteCommRingAddCommGroupModule