Theorems · Theorem · functional analysis

ContinuousLinearMap.reApplyInnerSelf_apply

∀ {𝕜 : Type u_1} {E : Type u_2} [inst : RCLike 𝕜] [inst_1 : SeminormedAddCommGroup E] [inst_2 : InnerProductSpace 𝕜 E]
  (T : E →L[𝕜] E) (x : E), T.reApplyInnerSelf x = RCLike.re (inner 𝕜 (T x) x)

Defined in

Mathlib.Analysis.InnerProductSpace.LinearMap

Cited by

1 results in Mathlib

Foundations

Depth 97 from the axioms · uses propext, Classical.choice, Quot.sound

Assumes

RCLikeSeminormedAddCommGroupInnerProductSpace