Theorems · Theorem · functional analysis
spectrum.unit_smul_eq_smul
∀ {R : Type u} {A : Type v} [inst : CommSemiring R] [inst_1 : Ring A] [inst_2 : Algebra R A] (a : A) (r : Rˣ),
spectrum R (r • a) = r • spectrum R a- Defined in
- Mathlib.Algebra.Algebra.Spectrum.Basic
- Cited by
- 2 results in Mathlib
- Foundations
- Depth 23 from the axioms · uses propext, Quot.sound
- Assumes
- CommSemiringRingAlgebra
Around this declaration
Dashed lines are statement dependencies; solid lines are citations in proofs.
Cites12
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
- CommSemiringstatement and proof · cited by 10,911
- Ringstatement and proof · cited by 7,463
- Unitsstatement and proof · cited by 2,804
- Set.extproof · cited by 2,266
- Units.valproof · cited by 1,966
- Set.smulSetstatement · cited by 608
- spectrumstatement and proof · cited by 510
- inv_smul_smulproof · cited by 76
- smul_inv_smulproof · cited by 53
- spectrum.smul_mem_smul_iffproof · cited by 2
Cited by2
Results whose statement or proof uses this declaration.
- SpectrumRestricts.smul_of_nonnegproof · cited by 1
- spectrum.smul_eq_smulproof · cited by 0