Theorems · Theorem · ring theory
Unitary.mem_iff_self_mul_star
∀ {R : Type u_1} [inst : CommMonoid R] [inst_1 : StarMul R] {U : R}, U ∈ unitary R ↔ U * star U = 1- Defined in
- Mathlib.Algebra.Star.Unitary
- Cited by
- 2 results in Mathlib
- Foundations
- Depth 23 from the axioms · uses propext, Quot.sound
- Assumes
- CommMonoidStarMul
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.
- Submonoidstatement · cited by 3,086
- CommMonoidstatement and proof · cited by 2,264
- mul_commproof · cited by 2,262
- Star.starstatement and proof · cited by 1,082
- unitarystatement · cited by 207
- StarMulstatement and proof · cited by 195
- Unitary.mem_iffproof · cited by 7
Cited by2
Results whose statement or proof uses this declaration.
- QuadraticAlgebra.norm_eq_one_iff_mem_unitaryproof · cited by 3
- Zsqrtd.norm_eq_one_iff_mem_unitaryproof · cited by 2