Theorems · Theorem · ring theory
Unitary.conjStarAlgAut_apply
∀ {S : Type u_1} {R : Type u_2} [inst : Semiring R] [inst_1 : StarMul R] [inst_2 : SMul S R]
[inst_3 : IsScalarTower S R R] [inst_4 : SMulCommClass S R R] (u : ↥(unitary R)) (x : R),
((Unitary.conjStarAlgAut S R) u) x = ↑u * x * star ↑u- Defined in
- Mathlib.Algebra.Star.UnitaryStarAlgAut
- Cited by
- 4 results in Mathlib
- Foundations
- Depth 33 from the axioms · uses propext, Classical.choice, Quot.sound
Around this declaration
Dashed lines are statement dependencies; solid lines are citations in proofs.
Cites11
Mathlib declarations this one mentions in its statement or cites explicitly in its proof. Plumbing is filtered out.
- DFunLike.coestatement · cited by 62,936
- Semiringstatement and proof · cited by 13,802
- IsScalarTowerstatement and proof · cited by 3,896
- MonoidHomstatement · cited by 3,629
- Submonoidstatement · cited by 3,086
- SMulCommClassstatement and proof · cited by 1,927
- Star.starstatement · cited by 1,082
- unitarystatement and proof · cited by 207
- StarMulstatement and proof · cited by 195
- StarAlgEquivstatement · cited by 132
- Unitary.conjStarAlgAutstatement · cited by 26
Cited by4
Results whose statement or proof uses this declaration.
- Matrix.IsHermitian.charpoly_eqproof · cited by 2
- Matrix.IsHermitian.rank_eq_rank_diagonalproof · cited by 1
- Matrix.IsHermitian.charpoly_cfc_eqproof · cited by 0
- Matrix.PosSemidef.trace_eq_zero_iffproof · cited by 0