Theorems · Theorem · functional analysis

Submodule.reflection_orthogonalComplement_singleton_eq_neg

∀ {𝕜 : Type u_1} {E : Type u_2} [inst : RCLike 𝕜] [inst_1 : NormedAddCommGroup E] [inst_2 : InnerProductSpace 𝕜 E]
  (v : E), (𝕜 ∙ v)ᗮ.reflection v = -v

The reflection in (𝕜 ∙ v)ᗮ of v is -v.

Defined in

Mathlib.Analysis.InnerProductSpace.Projection.Reflection

Cited by

2 results in Mathlib

Foundations

Depth 186 from the axioms · uses propext, Classical.choice, Quot.sound

Assumes

RCLikeNormedAddCommGroupInnerProductSpace