Theorems · Theorem · functional analysis
Submodule.range_starProjection
∀ {𝕜 : Type u_1} {E : Type u_2} [inst : RCLike 𝕜] [inst_1 : NormedAddCommGroup E] [inst_2 : InnerProductSpace 𝕜 E]
(U : Submodule 𝕜 E) [inst_3 : U.HasOrthogonalProjection], (↑U.starProjection).range = U- Cited by
- 1 results in Mathlib
- Foundations
- Depth 180 from the axioms · uses propext, Classical.choice, Quot.sound
Around this declaration
Dashed lines are statement dependencies; solid lines are citations in proofs.
Cites14
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 · cited by 18,349
- 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
- LinearMap.rangestatement and proof · cited by 893
- ContinuousLinearMap.toLinearMapstatement and proof · cited by 528
- Submodule.HasOrthogonalProjectionstatement and proof · cited by 245
- Submodule.extproof · cited by 204
- Submodule.orthogonalProjectionOntoproof · cited by 103
- Submodule.starProjectionstatement and proof · cited by 92
Cited by1
Results whose statement or proof uses this declaration.
- Submodule.ker_starProjectionproof · cited by 0