Theorems · Theorem · functional analysis

Submodule.IsOrtho.starProjection_comp_starProjection

∀ {𝕜 : Type u_1} {E : Type u_2} [inst : RCLike 𝕜] [inst_1 : NormedAddCommGroup E] [inst_2 : InnerProductSpace 𝕜 E]
  {U V : Submodule 𝕜 E} [inst_3 : U.HasOrthogonalProjection] [inst_4 : V.HasOrthogonalProjection],
  U ⟂ V → U.starProjection ∘SL V.starProjection = 0

Defined in: Mathlib.Analysis.InnerProductSpace.Projection.Basic
Cited by: 1 results in Mathlib
Foundations: Depth 183 from the axioms · uses propext, Classical.choice, Quot.sound
Assumes: RCLike NormedAddCommGroup InnerProductSpace Submodule.HasOrthogonalProjection Submodule.HasOrthogonalProjection

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Cites16

Mathlib declarations this one mentions in its statement or cites explicitly in its proof. Plumbing is filtered out.

RingHom.idstatement · cited by 18,349
NormedAddCommGroupstatement and proof · cited by 15,752
Submodulestatement and proof · cited by 7,192
ContinuousLinearMapstatement · cited by 5,352
InnerProductSpacestatement and proof · cited by 3,523
RCLikestatement and proof · cited by 2,829
ContinuousLinearMap.compstatement and proof · cited by 709
Submodule.HasOrthogonalProjectionstatement and proof · cited by 245
Submodule.orthogonalProjectionOntoproof · cited by 103
Submodule.starProjectionstatement · cited by 92
ContinuousLinearMap.comp.congr_simpproof · cited by 77
Submodule.subtypeLproof · cited by 53

Cited by1

Results whose statement or proof uses this declaration.

Submodule.starProjection_comp_starProjection_eq_zero_iffproof · cited by 0