Theorems · Theorem · functional analysis
LinearMap.isSymmetricProjection_iff_eq_coe_starProjection
∀ {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 ↔ ∃ K, ∃ (x : K.HasOrthogonalProjection), p = ↑K.starProjection- Cited by
- 1 results in Mathlib
- Foundations
- Depth 185 from the axioms · uses propext, Classical.choice, Quot.sound
Around this declaration
Dashed lines are statement dependencies; solid lines are citations in proofs.
Cites13
Mathlib declarations this one mentions in its statement or cites explicitly in its proof. Plumbing is filtered out.
- RingHom.idstatement and proof · cited by 18,349
- NormedAddCommGroupstatement and proof · cited by 15,752
- LinearMapstatement and proof · cited by 10,215
- Submodulestatement and proof · cited by 7,192
- InnerProductSpacestatement and proof · cited by 3,523
- RCLikestatement and proof · cited by 2,829
- LinearMap.rangeproof · cited by 893
- ContinuousLinearMap.toLinearMapstatement and proof · cited by 528
- Submodule.HasOrthogonalProjectionstatement and proof · cited by 245
- Submodule.starProjectionstatement and proof · cited by 92
- LinearMap.IsSymmetricProjectionstatement and proof · cited by 21
- Submodule.isSymmetricProjection_starProjectionproof · cited by 3
Cited by1
Results whose statement or proof uses this declaration.
- LinearMap.IsSymmetricProjection.le_iff_range_le_rangeproof · cited by 1