Theorems · Theorem · functional analysis

Submodule.toLinearEquiv_quotientEquivOrthogonal

∀ {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.toLinearEquiv = K.quotientEquivOfIsCompl Kᗮ ⋯

Defined in: Mathlib.Analysis.InnerProductSpace.ProdL2
Cited by: 0 results in Mathlib
Foundations: Depth 185 from the axioms · uses propext, Classical.choice, Quot.sound
Assumes: RCLike NormedAddCommGroup InnerProductSpace Submodule.HasOrthogonalProjection

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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
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
Submodule.orthogonalstatement · cited by 257
Submodule.HasOrthogonalProjectionstatement and proof · cited by 245
LinearIsometryEquiv.toLinearEquivstatement · cited by 107
Submodule.isCompl_orthogonalstatement · cited by 24
Submodule.quotientEquivOfIsComplstatement · cited by 23

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