Theorems · Theorem · functional analysis
LinearMap.IsSymmetricProjection.hasOrthogonalProjection_range
∀ {𝕜 : Type u_1} {E : Type u_2} [inst : RCLike 𝕜] [inst_1 : NormedAddCommGroup E] [inst_2 : InnerProductSpace 𝕜 E]
{p : E →ₗ[𝕜] E}, p.IsSymmetricProjection → p.range.HasOrthogonalProjection- Cited by
- 1 results in Mathlib
- Foundations
- Depth 173 from the axioms · uses propext, Classical.choice, Quot.sound
Around this declaration
Dashed lines are statement dependencies; solid lines are citations in proofs.
Cites15
Mathlib declarations this one mentions in its statement or cites explicitly in its proof. Plumbing is filtered out.
- DFunLike.coeproof · cited by 62,936
- RingHom.idstatement and proof · cited by 18,349
- NormedAddCommGroupstatement and proof · cited by 15,752
- LinearMapstatement and proof · cited by 10,215
- InnerProductSpacestatement and proof · cited by 3,523
- RCLikestatement and proof · cited by 2,829
- sub_selfproof · cited by 996
- LinearMap.rangestatement · cited by 893
- map_subproof · cited by 565
- Submodule.HasOrthogonalProjectionstatement · cited by 245
- IsIdempotentElem.eqproof · cited by 42
- LinearMap.IsSymmetricProjectionstatement and proof · cited by 21
Cited by1
Results whose statement or proof uses this declaration.
- LinearMap.isSymmetricProjection_iff_eq_coe_starProjection_rangeproof · cited by 1