Theorems · Theorem · functional analysis
selfAdjoint.expUnitary_coe
∀ {A : Type u_1} [inst : NormedRing A] [inst_1 : NormedAlgebra ℂ A] [inst_2 : StarRing A] [inst_3 : ContinuousStar A]
[inst_4 : CompleteSpace A] [inst_5 : StarModule ℂ A] (a : ↥(selfAdjoint A)),
↑(selfAdjoint.expUnitary a) = NormedSpace.exp (Complex.I • ↑a)- Cited by
- 8 results in Mathlib
- Foundations
- Depth 181 from the axioms · uses propext, Classical.choice, Quot.sound
Around this declaration
Dashed lines are statement dependencies; solid lines are citations in proofs.
Cites14
Mathlib declarations this one mentions in its statement or cites explicitly in its proof. Plumbing is filtered out.
- Complexstatement and proof · cited by 5,565
- AddSubgroupstatement · cited by 3,232
- Submonoidstatement · cited by 3,086
- CompleteSpacestatement and proof · cited by 2,532
- StarRingstatement and proof · cited by 1,686
- NormedAlgebrastatement and proof · cited by 1,165
- NormedRingstatement and proof · cited by 924
- Complex.Istatement · cited by 866
- StarModulestatement and proof · cited by 570
- ContinuousStarstatement and proof · cited by 543
- unitarystatement · cited by 207
- NormedSpace.expstatement · cited by 157
Cited by8
Results whose statement or proof uses this declaration.
- selfAdjoint.norm_sq_expUnitary_sub_oneproof · cited by 3
- expUnitary_argSelfAdjointproof · cited by 2
- Commute.expUnitary_addproof · cited by 1
- selfAdjoint.continuous_expUnitaryproof · cited by 0
- selfAdjoint.expUnitary_zeroproof · cited by 0
- isStarNormal_iff_forall_exp_mul_exp_mem_unitaryproof · cited by 0
- argSelfAdjoint_expUnitaryproof · cited by 0
- Unitary.isPathConnected_ballproof · cited by 0