Theorems · Theorem · functional analysis
Submodule.starProjection_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.starProjection v = 0- Cited by
- 0 results in Mathlib
- Foundations
- Depth 184 from the axioms · uses propext, Classical.choice, Quot.sound
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Cites14
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 and proof · cited by 1,504
- Submodule.orthogonalstatement and proof · cited by 257
- Submodule.starProjectionstatement · cited by 92
- Submodule.coe_eq_zeroproof · cited by 9
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