Theorems · Theorem · group theory
Matrix.mem_specialUnitaryGroup_iff
∀ {n : Type u} [inst : DecidableEq n] [inst_1 : Fintype n] {α : Type v} [inst_2 : CommRing α] [inst_3 : StarRing α]
{A : Matrix n n α}, A ∈ Matrix.specialUnitaryGroup n α ↔ A ∈ Matrix.unitaryGroup n α ∧ A.det = 1- Defined in
- Mathlib.LinearAlgebra.UnitaryGroup
- Cited by
- 0 results in Mathlib
- Foundations
- Depth 93 from the axioms · uses propext, Classical.choice, Quot.sound
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Cites8
Mathlib declarations this one mentions in its statement or cites explicitly in its proof. Plumbing is filtered out.
- CommRingstatement and proof · cited by 17,173
- Fintypestatement and proof · cited by 7,736
- Matrixstatement and proof · cited by 4,303
- Submonoidstatement · cited by 3,086
- StarRingstatement and proof · cited by 1,686
- Matrix.detstatement · cited by 665
- Matrix.unitaryGroupstatement · cited by 37
- Matrix.specialUnitaryGroupstatement · cited by 4
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