Theorems · Theorem · operator theory

LinearMap.IsSymmetricProjection.ext_iff

∀ {𝕜 : Type u_1} {E : Type u_2} [inst : RCLike 𝕜] [inst_1 : NormedAddCommGroup E] [inst_2 : InnerProductSpace 𝕜 E]
  {S T : E →ₗ[𝕜] E}, S.IsSymmetricProjection → T.IsSymmetricProjection → (S = T ↔ S.range = T.range)

Symmetric projections are equal iff their range are.

Defined in

Mathlib.Analysis.InnerProductSpace.Symmetric

Cited by

2 results in Mathlib

Foundations

Depth 173 from the axioms · uses propext, Classical.choice, Quot.sound

Assumes

RCLikeNormedAddCommGroupInnerProductSpace