Theorems · Theorem · linear algebra

LinearEquiv.piRing_symm_apply

∀ {R : Type u} {M : Type v} {ι : Type x} [inst : Semiring R] (S : Type u_4) [inst_1 : Fintype ι]
  [inst_2 : DecidableEq ι] [inst_3 : Semiring S] [inst_4 : AddCommMonoid M] [inst_5 : Module R M] [inst_6 : Module S M]
  [inst_7 : SMulCommClass R S M] (f : ι → M) (g : ι → R), ((LinearEquiv.piRing R M ι S).symm f) g = ∑ i, g i • f i

Defined in

Mathlib.LinearAlgebra.Pi

Cited by

1 results in Mathlib

Foundations

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

Assumes

SemiringFintypeDecidableEqSemiringAddCommMonoidModuleModuleSMulCommClass