Theorems · Theorem · functional analysis

Submodule.toLinearEquiv_orthogonalDecomposition

∀ {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.toLinearEquiv =
    (K.prodEquivOfIsCompl Kᗮ ⋯).symm ≪≫ₗ (WithLp.linearEquiv 2 𝕜 (↥K × ↥Kᗮ)).symm

Defined in: Mathlib.Analysis.InnerProductSpace.ProdL2
Cited by: 0 results in Mathlib
Foundations: Depth 225 from the axioms · uses propext, Classical.choice, Quot.sound
Assumes: RCLike NormedAddCommGroup InnerProductSpace Submodule.HasOrthogonalProjection

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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
InnerProductSpacestatement and proof · cited by 3,523
LinearEquivstatement · cited by 3,317
RCLikestatement and proof · cited by 2,829
LinearEquiv.symmstatement · cited by 1,461
WithLpstatement · cited by 345
LinearEquiv.transstatement · cited by 298
Submodule.orthogonalstatement · cited by 257
Submodule.HasOrthogonalProjectionstatement and proof · cited by 245

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