Theorems · Theorem · linear algebra

Module.Basis.groupSMul_apply

∀ {ι : Type u_1} {R : Type u_2} {M : Type u_4} [inst : Semiring R] [inst_1 : AddCommMonoid M] [inst_2 : Module R M]
  {G : Type u_5} [inst_3 : Group G] [inst_4 : DistribMulAction G R] [inst_5 : DistribMulAction G M]
  [inst_6 : IsScalarTower G R M] [inst_7 : SMulCommClass G R M] {v : Module.Basis ι R M} {w : ι → G} (i : ι),
  (v.groupSMul w) i = (w • ⇑v) i

Defined in

Mathlib.LinearAlgebra.Basis.SMul

Cited by

0 results in Mathlib

Foundations

Depth 89 from the axioms · uses propext, Classical.choice, Quot.sound

Assumes

SemiringAddCommMonoidModuleGroupDistribMulActionDistribMulActionIsScalarTowerSMulCommClass