Theorems · Theorem · functional analysis
Submodule.orthogonalProjectionOnto_orthogonalComplement_singleton_eq_zero
∀ {𝕜 : Type u_1} {E : Type u_2} [inst : RCLike 𝕜] [inst_1 : NormedAddCommGroup E] [inst_2 : InnerProductSpace 𝕜 E]
(v : E), (𝕜 ∙ v)ᗮ.orthogonalProjectionOnto v = 0The orthogonal projection onto (𝕜 ∙ v)ᗮ of v is zero.
- Cited by
- 3 results in Mathlib
- Foundations
- Depth 183 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.
- DFunLike.coestatement · cited by 62,936
- Setstatement · cited by 53,352
- RingHom.idstatement · cited by 18,349
- NormedAddCommGroupstatement and proof · cited by 15,752
- Submodulestatement · cited by 7,192
- ContinuousLinearMapstatement · cited by 5,352
- InnerProductSpacestatement and proof · cited by 3,523
- RCLikestatement and proof · cited by 2,829
- Submodule.spanstatement · cited by 1,504
- Submodule.orthogonalstatement · cited by 257
- Submodule.orthogonalProjectionOntostatement · cited by 103
- Submodule.mem_span_singleton_selfproof · cited by 59
Cited by3
Results whose statement or proof uses this declaration.
- stereo_right_invproof · cited by 1
- Submodule.orthogonalProjection_orthogonalComplement_singleton_eq_zeroproof · cited by 0
- Submodule.starProjection_orthogonalComplement_singleton_eq_zeroproof · cited by 0