Theorems · Theorem · functional analysis
spectrum.neg_eq
∀ {R : Type u} {A : Type v} [inst : CommRing R] [inst_1 : Ring A] [inst_2 : Algebra R A] (a : A),
-spectrum R a = spectrum R (-a)- Defined in
- Mathlib.Algebra.Algebra.Spectrum.Basic
- Cited by
- 4 results in Mathlib
- Foundations
- Depth 20 from the axioms · uses propext, Quot.sound
Around this declaration
Dashed lines are statement dependencies; solid lines are citations in proofs.
Cites10
Mathlib declarations this one mentions in its statement or cites explicitly in its proof. Plumbing is filtered out.
- Setstatement and proof · cited by 53,352
- CommRingstatement and proof · cited by 17,173
- Algebrastatement and proof · cited by 11,388
- Ringstatement and proof · cited by 7,463
- Compl.complproof · cited by 2,925
- spectrumstatement and proof · cited by 510
- Set.negstatement · cited by 168
- resolventSetproof · cited by 30
- Set.compl_negproof · cited by 2
- resolventSet_negproof · cited by 2
Cited by4
Results whose statement or proof uses this declaration.
- spectrum.singleton_sub_eqproof · cited by 2
- CFC.negPart_eq_negproof · cited by 1
- spectrum.sub_singleton_eqproof · cited by 0
- CFC.posPart_negPart_uniqueproof · cited by 0