Theorems · Theorem · functional analysis
Submodule.starProjection_apply_eq_zero_iff
∀ {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 : E}, K.starProjection v = 0 ↔ v ∈ Kᗮ- Cited by
- 0 results in Mathlib
- Foundations
- Depth 182 from the axioms · uses propext, Classical.choice, Quot.sound
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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.innerproof · cited by 1,089
- Submodule.orthogonalstatement and proof · cited by 257
- Submodule.HasOrthogonalProjectionstatement and proof · cited by 245
- Submodule.starProjectionstatement and proof · cited by 92
- inner_zero_rightproof · cited by 40
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