Theorems · Definition · linear algebra

Finsupp.domLCongr

{M : Type u_2} →
  {R : Type u_5} →
    [inst : Semiring R] →
      [inst_1 : AddCommMonoid M] →
        [inst_2 : Module R M] → {α₁ : Type u_9} → {α₂ : Type u_10} → α₁ ≃ α₂ → (α₁ →₀ M) ≃ₗ[R] α₂ →₀ M

An equivalence of domains induces a linear equivalence of finitely supported functions. This is Finsupp.domCongr as a LinearEquiv. See also LinearMap.funCongrLeft for the case of arbitrary functions.

Defined in

Mathlib.LinearAlgebra.Finsupp.LSum

Cited by

20 results in Mathlib

Foundations

Depth 80 from the axioms · uses propext, Classical.choice, Quot.sound

Assumes

SemiringAddCommMonoidModule