Theorems · Theorem · linear algebra
mem_unitary_iff_isStarNormal_and_realPart_sq_add_imaginaryPart_sq_eq_one
∀ {A : Type u_1} [inst : Ring A] [inst_1 : StarRing A] [inst_2 : Module ℂ A] [SMulCommClass ℂ A A] [IsScalarTower ℂ A A]
[inst_5 : StarModule ℂ A] {x : A}, x ∈ unitary A ↔ IsStarNormal x ∧ ↑(realPart x) ^ 2 + ↑(imaginaryPart x) ^ 2 = 1- Defined in
- Mathlib.LinearAlgebra.Complex.Module
- Cited by
- 0 results in Mathlib
- Foundations
- Depth 119 from the axioms · uses propext, Classical.choice, Quot.sound
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Mathlib declarations this one mentions in its statement or cites explicitly in its proof. Plumbing is filtered out.
- DFunLike.coestatement and proof · cited by 62,936
- Realstatement · cited by 25,697
- Modulestatement and proof · cited by 20,661
- RingHom.idstatement · cited by 18,349
- LinearMapstatement · cited by 10,215
- Ringstatement and proof · cited by 7,463
- Complexstatement and proof · cited by 5,565
- IsScalarTowerstatement and proof · cited by 3,896
- AddSubgroupstatement · cited by 3,232
- Submonoidstatement · cited by 3,086
- SMulCommClassstatement and proof · cited by 1,927
- StarRingstatement and proof · cited by 1,686
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