Theorems · Theorem · linear algebra

Module.Basis.mk_apply

∀ {ι : Type u_1} {R : Type u_3} {M : Type u_5} [inst : Semiring R] [inst_1 : AddCommMonoid M] [inst_2 : Module R M]
  {v : ι → M} (hli : LinearIndependent R v) (hsp : ⊤ ≤ Submodule.span R (Set.range v)) (i : ι),
  (Module.Basis.mk hli hsp) i = v i

Defined in

Mathlib.LinearAlgebra.Basis.Basic

Cited by

9 results in Mathlib

Foundations

Depth 88 from the axioms · uses propext, Classical.choice, Quot.sound

Assumes

SemiringAddCommMonoidModule