Theorems · Theorem · functional analysis
Submodule.starProjection_inner_eq_zero
∀ {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] (v w : E), w ∈ K → inner 𝕜 (v - K.starProjection v) w = 0The characterization of the orthogonal projection.
- Cited by
- 8 results in Mathlib
- Foundations
- Depth 177 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
- Inner.innerstatement · cited by 1,089
- Submodule.orthogonalproof · cited by 257
- Submodule.HasOrthogonalProjectionstatement and proof · cited by 245
- Submodule.starProjectionstatement · cited by 92
- IsCompl.symmproof · cited by 80
Cited by8
Results whose statement or proof uses this declaration.
- Submodule.sub_starProjection_mem_orthogonalproof · cited by 8
- Submodule.eq_starProjection_of_mem_of_inner_eq_zeroproof · cited by 6
- Submodule.inner_orthogonalProjectionOnto_eq_of_mem_rightproof · cited by 5
- Submodule.orthogonalProjectionOnto_comp_subtypeL_eq_zero_iffproof · cited by 2
- LinearIsometry.map_starProjectionproof · cited by 1
- Submodule.starProjection_minimalproof · cited by 1
- MeasureTheory.inner_condExpL2_eq_inner_funproof · cited by 0
- Submodule.orthogonalProjectionFn_inner_eq_zeroproof · cited by 0