Theorems · Theorem · functional analysis

Submodule.smul_starProjection_singleton

∀ (𝕜 : Type u_1) {E : Type u_2} [inst : RCLike 𝕜] [inst_1 : NormedAddCommGroup E] [inst_2 : InnerProductSpace 𝕜 E]
  {v : E} (w : E), ↑(‖v‖ ^ 2) • (𝕜 ∙ v).starProjection w = inner 𝕜 v w • v

Defined in

Mathlib.Analysis.InnerProductSpace.Projection.Basic

Cited by

2 results in Mathlib

Foundations

Depth 180 from the axioms · uses propext, Classical.choice, Quot.sound

Assumes

RCLikeNormedAddCommGroupInnerProductSpace