Theorems · Theorem · functional analysis

InnerProductSpace.rankOne_comp_rankOne

∀ {𝕜 : Type u_4} {E : Type u_5} {F : Type u_6} {G : Type u_7} [inst : RCLike 𝕜] [inst_1 : SeminormedAddCommGroup E]
  [inst_2 : NormedSpace 𝕜 E] [inst_3 : SeminormedAddCommGroup F] [inst_4 : InnerProductSpace 𝕜 F]
  [inst_5 : SeminormedAddCommGroup G] [inst_6 : InnerProductSpace 𝕜 G] (x : E) (y z : F) (w : G),
  ((InnerProductSpace.rankOne 𝕜) x) y ∘SL ((InnerProductSpace.rankOne 𝕜) z) w =
    inner 𝕜 y z • ((InnerProductSpace.rankOne 𝕜) x) w

Defined in

Mathlib.Analysis.InnerProductSpace.LinearMap

Cited by

0 results in Mathlib

Foundations

Depth 179 from the axioms · uses propext, Classical.choice, Quot.sound

Assumes

RCLikeSeminormedAddCommGroupNormedSpaceSeminormedAddCommGroupInnerProductSpaceSeminormedAddCommGroupInnerProductSpace