Theorems · Theorem · functional analysis
Submodule.starProjection_orthogonal_val
∀ {𝕜 : Type u_1} {E : Type u_2} [inst : RCLike 𝕜] [inst_1 : NormedAddCommGroup E] [inst_2 : InnerProductSpace 𝕜 E]
{K : Submodule 𝕜 E} [inst_3 : K.HasOrthogonalProjection] (u : E), Kᗮ.starProjection u = u - K.starProjection u- Cited by
- 7 results in Mathlib
- Foundations
- Depth 181 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.coestatement and proof · cited by 62,936
- RingHom.idstatement · cited by 18,349
- NormedAddCommGroupstatement and proof · cited by 15,752
- Submodulestatement and proof · cited by 7,192
- ContinuousLinearMapstatement · cited by 5,352
- InnerProductSpacestatement and proof · cited by 3,523
- RCLikestatement and proof · cited by 2,829
- sub_add_cancelproof · cited by 344
- Submodule.orthogonalstatement · cited by 257
- Submodule.HasOrthogonalProjectionstatement and proof · cited by 245
- Submodule.orthogonalProjectionOntoproof · cited by 103
- Submodule.starProjectionstatement and proof · cited by 92
Cited by7
Results whose statement or proof uses this declaration.
- Submodule.starProjection_add_starProjection_orthogonalproof · cited by 3
- Submodule.orthogonalProjectionOnto_orthogonalproof · cited by 2
- Submodule.re_inner_starProjection_eq_normSqproof · cited by 1
- Submodule.mem_iff_norm_starProjectionproof · cited by 1
- Submodule.reflection_orthogonal_applyproof · cited by 1
- Submodule.sndL_comp_coe_orthogonalDecompositionproof · cited by 0
- Submodule.orthogonalProjectionFn_norm_sqproof · cited by 0