Theorems · Definition · linear algebra

Module.Basis.repr

{ι : Type u_1} →
  {R : Type u_3} →
    {M : Type u_6} →
      [inst : Semiring R] → [inst_1 : AddCommMonoid M] → [inst_2 : Module R M] → Module.Basis ι R M → M ≃ₗ[R] ι →₀ R

repr is the linear equivalence sending a vector x to its coordinates: the cs such that x = ∑ i, c i.

Defined in

Mathlib.LinearAlgebra.Basis.Defs

Cited by

498 results in Mathlib

Foundations

Depth 73 from the axioms, rests on 1,027 definitions · uses propext, Classical.choice, Quot.sound

Assumes

SemiringAddCommMonoidModule