Theorems · Theorem · linear algebra

DFinsupp.sum_mapRange_index.linearMap

∀ {ι : Type u_1} {R : Type u_3} {N : Type u_6} [inst : Semiring R] [inst_1 : AddCommMonoid N] [inst_2 : Module R N]
  {β₁ : ι → Type u_8} {β₂ : ι → Type u_9} [inst_3 : (i : ι) → AddCommMonoid (β₁ i)]
  [inst_4 : (i : ι) → AddCommMonoid (β₂ i)] [inst_5 : (i : ι) → Module R (β₁ i)] [inst_6 : (i : ι) → Module R (β₂ i)]
  [inst_7 : DecidableEq ι] {f : (i : ι) → β₁ i →ₗ[R] β₂ i} {h : (i : ι) → β₂ i →ₗ[R] N} {l : Π₀ (i : ι), β₁ i},
  ((DFinsupp.lsum ℕ) h) ((DFinsupp.mapRange.linearMap f) l) = ((DFinsupp.lsum ℕ) fun i => h i ∘ₗ f i) l

Defined in

Mathlib.LinearAlgebra.DFinsupp

Cited by

0 results in Mathlib

Foundations

Depth 87 from the axioms · uses propext, Classical.choice, Quot.sound

Assumes

SemiringAddCommMonoidModuleAddCommMonoidAddCommMonoidModuleModuleDecidableEq