Theorems · Theorem · linear algebra

Finsupp.mapRange.linearEquiv_apply

∀ {α : Type u_1} {M : Type u_2} {N : Type u_3} {R : Type u_5} {R₂ : Type u_6} [inst : Semiring R] [inst_1 : Semiring R₂]
  [inst_2 : AddCommMonoid M] [inst_3 : Module R M] [inst_4 : AddCommMonoid N] [inst_5 : Module R₂ N] {σ₁₂ : R →+* R₂}
  {σ₂₁ : R₂ →+* R} [inst_6 : RingHomInvPair σ₁₂ σ₂₁] [inst_7 : RingHomInvPair σ₂₁ σ₁₂] (e : M ≃ₛₗ[σ₁₂] N) (g : α →₀ M),
  (Finsupp.mapRange.linearEquiv e) g = Finsupp.mapRange ⇑e ⋯ g

Defined in

Mathlib.LinearAlgebra.Finsupp.Defs

Cited by

14 results in Mathlib

Foundations

Depth 76 from the axioms · uses propext, Classical.choice, Quot.sound

Assumes

SemiringSemiringAddCommMonoidModuleAddCommMonoidModuleRingHomInvPairRingHomInvPair