Theorems · Theorem · linear algebra

basisOfLinearIndependentOfCardEqFinrank_repr_apply

∀ {K : Type u} {V : Type v} [inst : DivisionRing K] [inst_1 : AddCommGroup V] [inst_2 : Module K V] {ι : Type u_1}
  [inst_3 : Fintype ι] [inst_4 : Nonempty ι] {b : ι → V} (lin_ind : LinearIndependent K b)
  (card_eq : Fintype.card ι = Module.finrank K V) (x : V),
  (basisOfLinearIndependentOfCardEqFinrank lin_ind card_eq).repr x =
    lin_ind.repr ((LinearMap.codRestrict (Submodule.span K (Set.range b)) LinearMap.id ⋯) x)

Defined in

Mathlib.LinearAlgebra.FiniteDimensional.Lemmas

Cited by

0 results in Mathlib

Foundations

Depth 122 from the axioms · uses propext, Classical.choice, Quot.sound

Assumes

DivisionRingAddCommGroupModuleFintypeNonempty