Theorems · Theorem · group theory
Matrix.transpose_mem_unitaryGroup_iff
∀ {n : Type u} [inst : DecidableEq n] [inst_1 : Fintype n] {α : Type v} [inst_2 : CommRing α] [inst_3 : StarRing α]
{U : Matrix n n α}, U.transpose ∈ Matrix.unitaryGroup n α ↔ U ∈ Matrix.unitaryGroup n α- Defined in
- Mathlib.LinearAlgebra.UnitaryGroup
- Cited by
- 0 results in Mathlib
- Foundations
- Depth 89 from the axioms · uses propext, Classical.choice, Quot.sound
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Cites14
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
- Star.starproof · cited by 1,082
- Matrix.transposestatement and proof · cited by 389
- Matrix.unitaryGroupstatement and proof · cited by 37
- Matrix.transpose_transposeproof · cited by 33
- Matrix.transpose_oneproof · cited by 22
- Matrix.transpose_mulproof · cited by 14
- Matrix.mem_unitaryGroup_iffproof · cited by 3
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