Theorems · Theorem · functional analysis

LinearIsometry.extend_apply

∀ {𝕜 : Type u_3} [inst : RCLike 𝕜] {V : Type u_7} [inst_1 : NormedAddCommGroup V] [inst_2 : InnerProductSpace 𝕜 V]
  [inst_3 : FiniteDimensional 𝕜 V] {S : Submodule 𝕜 V} (L : ↥S →ₗᵢ[𝕜] V) (s : ↥S), L.extend ↑s = L s

Defined in

Mathlib.Analysis.InnerProductSpace.PiL2

Cited by

0 results in Mathlib

Foundations

Depth 242 from the axioms · uses propext, Classical.choice, Quot.sound

Assumes

RCLikeNormedAddCommGroupInnerProductSpaceFiniteDimensional