Theorems · Theorem · functional analysis
Submodule.isOrtho_iff_inner_eq
∀ {𝕜 : Type u_1} {E : Type u_2} [inst : RCLike 𝕜] [inst_1 : NormedAddCommGroup E] [inst_2 : InnerProductSpace 𝕜 E]
{U V : Submodule 𝕜 E}, U ⟂ V ↔ ∀ u ∈ U, ∀ v ∈ V, inner 𝕜 u v = 0- Cited by
- 2 results in Mathlib
- Foundations
- Depth 163 from the axioms · uses propext, Classical.choice, Quot.sound
Around this declaration
Dashed lines are statement dependencies; solid lines are citations in proofs.
Cites7
Mathlib declarations this one mentions in its statement or cites explicitly in its proof. Plumbing is filtered out.
- NormedAddCommGroupstatement and proof · cited by 15,752
- Submodulestatement and proof · cited by 7,192
- InnerProductSpacestatement and proof · cited by 3,523
- RCLikestatement and proof · cited by 2,829
- Inner.innerstatement · cited by 1,089
- Submodule.IsOrthostatement · cited by 50
- inner_eq_zero_symmproof · cited by 12
Cited by2
Results whose statement or proof uses this declaration.
- Submodule.isSymmetric_projection_iffproof · cited by 2
- Submodule.IsOrtho.comapproof · cited by 1