Theorems · Theorem · functional analysis
Submodule.coe_quotientEquivOrthogonal_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.quotientEquivOrthogonal.symm = ⇑(K.quotientEquivOfIsCompl Kᗮ ⋯).symm- Cited by
- 0 results in Mathlib
- Foundations
- Depth 185 from the axioms · uses propext, Classical.choice, Quot.sound
Around this declaration
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Cites16
Mathlib declarations this one mentions in its statement or cites explicitly in its proof. Plumbing is filtered out.
- DFunLike.coestatement · cited by 62,936
- RingHom.idstatement · cited by 18,349
- NormedAddCommGroupstatement and proof · cited by 15,752
- Submodulestatement and proof · cited by 7,192
- InnerProductSpacestatement and proof · cited by 3,523
- LinearEquivstatement · cited by 3,317
- RCLikestatement and proof · cited by 2,829
- HasQuotient.Quotientstatement · cited by 2,301
- LinearEquiv.symmstatement · cited by 1,461
- LinearIsometryEquivstatement · cited by 748
- LinearIsometryEquiv.symmstatement · cited by 287
- Submodule.orthogonalstatement · cited by 257
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