Theorems · Theorem · functional analysis

InnerProductSpace.comp_rankOne

∀ {𝕜 : Type u_4} {E : Type u_5} {F : Type u_6} [inst : RCLike 𝕜] [inst_1 : SeminormedAddCommGroup E]
  [inst_2 : NormedSpace 𝕜 E] [inst_3 : SeminormedAddCommGroup F] [inst_4 : InnerProductSpace 𝕜 F] {G : Type u_8}
  [inst_5 : SeminormedAddCommGroup G] [inst_6 : NormedSpace 𝕜 G] (x : E) (y : F) (f : E →L[𝕜] G),
  f ∘SL ((InnerProductSpace.rankOne 𝕜) x) y = ((InnerProductSpace.rankOne 𝕜) (f x)) y

Defined in

Mathlib.Analysis.InnerProductSpace.LinearMap

Cited by

3 results in Mathlib

Foundations

Depth 178 from the axioms · uses propext, Classical.choice, Quot.sound

Assumes

RCLikeSeminormedAddCommGroupNormedSpaceSeminormedAddCommGroupInnerProductSpaceSeminormedAddCommGroupNormedSpace