Theorems · Theorem · commutative algebra
spectralValue_le_one_iff
∀ {R : Type u_1} [inst : NormedDivisionRing R] {P : Polynomial R},
P.Monic → (spectralValue P ≤ 1 ↔ ∀ (n : ℕ), ‖P.coeff n‖ ≤ 1)The spectral value of a monic polynomial P is less than or equal to one if and only
if all of its coefficients have norm less than or equal to 1.
- Cited by
- 0 results in Mathlib
- Foundations
- Depth 199 from the axioms · uses propext, Classical.choice, Quot.sound
- Assumes
- NormedDivisionRing
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Cites30
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
- Norm.normstatement and proof · cited by 5,413
- LE.le.transproof · cited by 3,151
- iSupproof · cited by 2,415
- le_reflproof · cited by 2,061
- le_of_ltproof · cited by 1,175
- Polynomial.natDegreeproof · cited by 1,105
- Polynomial.coeffstatement and proof · cited by 1,045
- norm_nonnegproof · cited by 725
- one_divproof · cited by 624
- Polynomial.Monicstatement and proof · cited by 461
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