Theorems · Theorem · ring theory
IsSelfAdjoint.all
∀ {R : Type u_1} [inst : Star R] [TrivialStar R] (r : R), IsSelfAdjoint rAll elements are self-adjoint when star is trivial.
- Defined in
- Mathlib.Algebra.Star.SelfAdjoint
- Cited by
- 5 results in Mathlib
- Foundations
- Depth 3 from the axioms · uses no axioms
- Assumes
- StarTrivialStar
Around this declaration
Dashed lines are statement dependencies; solid lines are citations in proofs.
Cites4
Mathlib declarations this one mentions in its statement or cites explicitly in its proof. Plumbing is filtered out.
- IsSelfAdjointstatement · cited by 545
- Starstatement and proof · cited by 496
- TrivialStarstatement and proof · cited by 66
- TrivialStar.star_trivialproof · cited by 26
Cited by5
Results whose statement or proof uses this declaration.
- CFC.posPart_smulproof · cited by 2
- SpectrumRestricts.nnreal_iff_nnnormproof · cited by 2
- CStarAlgebra.star_left_conjugate_le_norm_smulproof · cited by 1
- isSelfAdjoint_mapproof · cited by 0
- Matrix.isHermitian_diagonalproof · cited by 0