Theorems · Theorem · functional analysis
ClosedSubmodule.mulI_orthogonal_eq_symplComp
∀ {H : Type u_1} [inst : NormedAddCommGroup H] [ipc : InnerProductSpace ℂ H] (S : ClosedSubmodule ℝ H),
Sᗮ.mulI = S.symplComp- Cited by
- 2 results in Mathlib
- Foundations
- Depth 184 from the axioms · uses propext, Classical.choice, Quot.sound
Around this declaration
Dashed lines are statement dependencies; solid lines are citations in proofs.
Cites42
Mathlib declarations this one mentions in its statement or cites explicitly in its proof. Plumbing is filtered out.
- Realstatement and proof · cited by 25,697
- NormedAddCommGroupstatement and proof · cited by 15,752
- Complexstatement and proof · cited by 5,565
- InnerProductSpacestatement and proof · cited by 3,523
- one_mulproof · cited by 2,841
- Unitsproof · cited by 2,804
- Set.extproof · cited by 2,266
- Units.valproof · cited by 1,966
- MulZeroClass.zero_mulproof · cited by 1,625
- Inner.innerproof · cited by 1,089
- neg_negproof · cited by 960
- Complex.reproof · cited by 882
Cited by2
Results whose statement or proof uses this declaration.
- ClosedSubmodule.mulI_symplCompproof · cited by 1
- ClosedSubmodule.mulI_orthogonalproof · cited by 0