Theorems · Definition · ring theory
unitary
(R : Type u_1) → [inst : Monoid R] → [StarMul R] → Submonoid R
In a \-monoid, `unitary R` is the submonoid consisting of all the elements `U` of
`R` such that `star U U = 1 and U * star U = 1`.
- Defined in
- Mathlib.Algebra.Star.Unitary
- Cited by
- 207 results in Mathlib
- Foundations
- Depth 21 from the axioms, rests on 125 definitions · uses propext, Quot.sound
Around this declaration
Dashed lines are statement dependencies; solid lines are citations in proofs.
Cites5
Mathlib declarations this one mentions in its statement or cites explicitly in its proof. Plumbing is filtered out.
- Set.ofPredproof · cited by 6,101
- Monoidstatement and proof · cited by 3,887
- Submonoidstatement · cited by 3,086
- Star.starproof · cited by 1,082
- StarMulstatement and proof · cited by 195
Cited by227
Results whose statement or proof uses this declaration.
- Pell.Solution₁proof · cited by 50
- Matrix.unitaryGroupproof · cited by 37
- Unitary.conjStarAlgAutstatement and proof · cited by 26
- pinGroupproof · cited by 25
- selfAdjoint.expUnitarystatement · cited by 19
- Unitary.toUnitsstatement and proof · cited by 18
- Unitary.argSelfAdjointstatement and proof · cited by 13
- Unitary.star_mul_self_of_memstatement and proof · cited by 13
- Matrix.IsHermitian.spectral_theoremstatement · cited by 10
- Unitary.mapstatement · cited by 10
- Unitary.mulRightstatement and proof · cited by 9
- selfAdjoint.expUnitary_coestatement · cited by 8
Showing the 200 most cited of 227.