Theorems · Theorem · functional analysis
Submodule.isOrtho_orthogonal_right
∀ {𝕜 : Type u_1} {E : Type u_2} [inst : RCLike 𝕜] [inst_1 : NormedAddCommGroup E] [inst_2 : InnerProductSpace 𝕜 E]
(U : Submodule 𝕜 E), U ⟂ Uᗮ- Cited by
- 4 results in Mathlib
- Foundations
- Depth 167 from the axioms · uses propext, Classical.choice, Quot.sound
Around this declaration
Dashed lines are statement dependencies; solid lines are citations in proofs.
Cites7
Mathlib declarations this one mentions in its statement or cites explicitly in its proof. Plumbing is filtered out.
- NormedAddCommGroupstatement and proof · cited by 15,752
- Submodulestatement and proof · cited by 7,192
- InnerProductSpacestatement and proof · cited by 3,523
- RCLikestatement and proof · cited by 2,829
- Submodule.orthogonalstatement · cited by 257
- Submodule.IsOrthostatement · cited by 50
- Submodule.le_orthogonal_orthogonalproof · cited by 7
Cited by4
Results whose statement or proof uses this declaration.
- LinearMap.IsIdempotentElem.isSymmetric_iff_orthogonal_rangeproof · cited by 4
- LinearMap.IsSymmetric.orthogonalComplement_iSup_eigenspacesproof · cited by 2
- Affine.Simplex.vectorSpan_isOrtho_altitude_directionproof · cited by 2
- Submodule.isOrtho_orthogonal_leftproof · cited by 0