Theorems · Definition · linear algebra

Module.Basis.equivFun

{ι : Type u_1} →
  {R : Type u_3} →
    {M : Type u_6} →
      [inst : Semiring R] →
        [inst_1 : AddCommMonoid M] → [inst_2 : Module R M] → [Finite ι] → Module.Basis ι R M → M ≃ₗ[R] ι → R

A module over R with a finite basis is linearly equivalent to functions from its basis to R.

Defined in

Mathlib.LinearAlgebra.Basis.Defs

Cited by

88 results in Mathlib

Foundations

Depth 74 from the axioms · uses propext, Classical.choice, Quot.sound

Assumes

SemiringAddCommMonoidModuleFinite