Theorems · Theorem · functional analysis
NonnegSpectrumClass.iff_spectrum_nonneg
∀ {𝕜 : Type u_3} {A : Type u_4} [inst : Semifield 𝕜] [inst_1 : LinearOrder 𝕜] [inst_2 : Ring A]
[inst_3 : PartialOrder A] [inst_4 : Algebra 𝕜 A],
NonnegSpectrumClass 𝕜 A ↔ ∀ (a : A), 0 ≤ a → ∀ x ∈ spectrum 𝕜 a, 0 ≤ x- Cited by
- 1 results in Mathlib
- Foundations
- Depth 46 from the axioms · uses propext, Classical.choice, Quot.sound
Around this declaration
Dashed lines are statement dependencies; solid lines are citations in proofs.
Cites11
Mathlib declarations this one mentions in its statement or cites explicitly in its proof. Plumbing is filtered out.
- Setstatement · cited by 53,352
- Algebrastatement and proof · cited by 11,388
- LinearOrderstatement and proof · cited by 8,572
- Ringstatement and proof · cited by 7,463
- PartialOrderstatement and proof · cited by 6,410
- spectrumstatement and proof · cited by 510
- Semifieldstatement and proof · cited by 439
- quasispectrumproof · cited by 292
- NonnegSpectrumClassstatement and proof · cited by 292
- Set.union_singletonproof · cited by 107
- quasispectrum_eq_spectrum_union_zeroproof · cited by 8
Cited by1
Results whose statement or proof uses this declaration.
- NonnegSpectrumClass.of_spectrum_nonnegproof · cited by 0