Theorems · Theorem · functional analysis
Submodule.coe_orthogonalDecomposition_symm
∀ {𝕜 : Type u_1} {E : Type u_4} [inst : RCLike 𝕜] [inst_1 : NormedAddCommGroup E] [inst_2 : InnerProductSpace 𝕜 E]
(K : Submodule 𝕜 E) [inst_3 : K.HasOrthogonalProjection],
↑↑K.orthogonalDecomposition.symm = K.subtypeL.coprod Kᗮ.subtypeL ∘SL ↑(WithLp.prodContinuousLinearEquiv 2 𝕜 ↥K ↥Kᗮ)- Cited by
- 0 results in Mathlib
- Foundations
- Depth 225 from the axioms · uses propext, Classical.choice, Quot.sound
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Cites18
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
- ENNRealstatement · cited by 9,879
- 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 · cited by 709
- ContinuousLinearEquiv.toContinuousLinearMapstatement · cited by 448
- WithLpstatement · cited by 345
- LinearIsometryEquiv.symmstatement · cited by 287
- Submodule.orthogonalstatement · cited by 257
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