Theorems · Theorem · linear algebra

Finsupp.linearCombination_smul

∀ {α : Type u_1} {M : Type u_2} (R : Type u_5) {S : Type u_6} [inst : Semiring R] [inst_1 : Semiring S]
  [inst_2 : AddCommMonoid M] [inst_3 : Module R M] {α' : Type u_7} {v : α → M} [inst_4 : Module R S]
  [inst_5 : Module S M] [inst_6 : IsScalarTower R S M] {w : α' → S},
  (Finsupp.linearCombination R fun i => w i.2 • v i.1) =
    ↑R (Finsupp.linearCombination S v) ∘ₗ
      Finsupp.mapRange.linearMap (Finsupp.linearCombination R w) ∘ₗ ↑(Finsupp.curryLinearEquiv R)

Defined in

Mathlib.LinearAlgebra.Finsupp.LinearCombination

Cited by

1 results in Mathlib

Foundations

Depth 86 from the axioms · uses propext, Classical.choice, Quot.sound

Assumes

SemiringSemiringAddCommMonoidModuleModuleModuleIsScalarTower