Theorems · Theorem · commutative algebra
spectralValue_eq_zero_iff
∀ {R : Type u_1} [inst : NormedRing R] [Nontrivial R] {p : Polynomial R},
p.Monic → (spectralValue p = 0 ↔ p = Polynomial.X ^ p.natDegree)The spectral value of p equals zero if and only if p is of the form X ^ n.
- Cited by
- 1 results in Mathlib
- Foundations
- Depth 197 from the axioms · uses propext, Classical.choice, Quot.sound
- Assumes
- NormedRingNontrivial
Around this declaration
Dashed lines are statement dependencies; solid lines are citations in proofs.
Cites24
Mathlib declarations this one mentions in its statement or cites explicitly in its proof. Plumbing is filtered out.
- Realstatement and proof · cited by 25,697
- Polynomialstatement and proof · cited by 5,681
- LE.le.transproof · cited by 3,151
- Nontrivialstatement and proof · cited by 2,416
- le_antisymmproof · cited by 2,068
- Polynomial.Xstatement and proof · cited by 1,639
- Polynomial.natDegreestatement and proof · cited by 1,105
- Polynomial.coeffproof · cited by 1,045
- NormedRingstatement and proof · cited by 924
- norm_nonnegproof · cited by 725
- Eq.leproof · cited by 605
- Polynomial.Monicstatement and proof · cited by 461
Cited by1
Results whose statement or proof uses this declaration.
- spectralNorm_zero_ltproof · cited by 3