Theorems · Theorem · functional analysis

Module.Basis.constrL_apply

∀ {𝕜 : Type u} [hnorm : NontriviallyNormedField 𝕜] {E : Type v} [inst : AddCommGroup E] [inst_1 : Module 𝕜 E]
  [inst_2 : TopologicalSpace E] [inst_3 : IsTopologicalAddGroup E] [inst_4 : ContinuousSMul 𝕜 E] {F : Type w}
  [inst_5 : AddCommGroup F] [inst_6 : Module 𝕜 F] [inst_7 : TopologicalSpace F] [inst_8 : IsTopologicalAddGroup F]
  [inst_9 : ContinuousSMul 𝕜 F] [inst_10 : CompleteSpace 𝕜] [inst_11 : T2Space E] {ι : Type u_2} [inst_12 : Fintype ι]
  (v : Module.Basis ι 𝕜 E) (f : ι → F) (e : E), (v.constrL f) e = ∑ i, v.equivFun e i • f i

Defined in

Mathlib.Topology.Algebra.Module.FiniteDimension

Cited by

0 results in Mathlib

Foundations

Depth 172 from the axioms · uses propext, Classical.choice, Quot.sound

Assumes

NontriviallyNormedFieldAddCommGroupModuleTopologicalSpaceIsTopologicalAddGroupContinuousSMulAddCommGroupModuleTopologicalSpaceIsTopologicalAddGroupContinuousSMulCompleteSpaceT2SpaceFintype