Theorems · Theorem · functional analysis

InnerProductSpace.rankOne_def

∀ {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] (x : E) (y : F),
  ((InnerProductSpace.rankOne 𝕜) x) y = ((innerSL 𝕜) y).smulRight x

Defined in

Mathlib.Analysis.InnerProductSpace.LinearMap

Cited by

2 results in Mathlib

Foundations

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

Assumes

RCLikeSeminormedAddCommGroupNormedSpaceSeminormedAddCommGroupInnerProductSpace