Theorems · Theorem · linear algebra

Fintype.linearCombination_apply_single

∀ {α : Type u_1} {M : Type u_2} (R : Type u_3) [inst : Fintype α] [inst_1 : Semiring R] [inst_2 : AddCommMonoid M]
  [inst_3 : Module R M] (v : α → M) [inst_4 : DecidableEq α] (i : α) (r : R),
  (Fintype.linearCombination R v) (Pi.single i r) = r • v i

Defined in

Mathlib.LinearAlgebra.Finsupp.LinearCombination

Cited by

3 results in Mathlib

Foundations

Depth 72 from the axioms · uses propext, Classical.choice, Quot.sound

Assumes

FintypeSemiringAddCommMonoidModuleDecidableEq