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Theorems · Theorem · functional analysis

Submodule.HasOrthogonalProjection.exists_orthogonal

∀ {𝕜 : Type u_1} {E : Type u_2} {inst : RCLike 𝕜} {inst_1 : NormedAddCommGroup E} {inst_2 : InnerProductSpace 𝕜 E}
  {K : Submodule 𝕜 E} [self : K.HasOrthogonalProjection] (v : E), ∃ w ∈ K, v - w ∈ Kᗮ
Defined in
Mathlib.Analysis.InnerProductSpace.Projection.Basic
Cited by
1 results in Mathlib
Foundations
Depth 162 from the axioms · uses propext, Classical.choice, Quot.sound
Assumes
Submodule.HasOrthogonalProjection
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Around this declaration

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Submodule.isCompl_orthogonal · cited by 24Submodule.isCompl_orthogo…NormedAddCommGroup · cited by 15752NormedAddCommGroupSubmodule · cited by 7192SubmoduleInnerProductSpace · cited by 3523InnerProductSpaceRCLike · cited by 2829RCLikeSubmodule.orthogonal · cited by 257Submodule.orthogonalSubmodule.HasOrthogonalProjection · cited by 245Submodule.HasOrthogonalPr…HasOrthogonalProjection.exist…CITED BYCITES

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