Theorems · Definition · commutative algebra
spectralValue
{R : Type u_1} → [inst : SeminormedRing R] → Polynomial R → ℝThe spectral value of a polynomial in R[X], where R is a seminormed ring. One motivation
for the spectral value: if the norm on R is nonarchimedean, and if a monic polynomial
splits into linear factors, then its spectral value is the norm of its largest root.
See max_norm_root_eq_spectralValue.
- Cited by
- 13 results in Mathlib
- Foundations
- Depth 194 from the axioms · uses propext, Classical.choice, Quot.sound
- Assumes
- SeminormedRing
Around this declaration
Dashed lines are statement dependencies; solid lines are citations in proofs.
Cites5
Mathlib declarations this one mentions in its statement or cites explicitly in its proof. Plumbing is filtered out.
- Realstatement · cited by 25,697
- Polynomialstatement and proof · cited by 5,681
- iSupproof · cited by 2,415
- SeminormedRingstatement and proof · cited by 446
- spectralValueTermsproof · cited by 8
Cited by14
Results whose statement or proof uses this declaration.
- spectralNormproof · cited by 31
- spectralNorm_zero_ltproof · cited by 3
- norm_root_le_spectralValuestatement and proof · cited by 3
- spectralNorm_extendsproof · cited by 3
- spectralValue_X_powstatement · cited by 2
- spectralValue_nonnegstatement · cited by 2
- spectralNorm_zeroproof · cited by 1
- spectralNorm.eq_of_towerproof · cited by 1
- spectralValue_X_sub_Cstatement · cited by 1
- spectralValue_eq_zero_iffstatement and proof · cited by 1
- spectralNorm.spectralMulAlgNorm_eq_of_mem_rootsproof · cited by 1
- max_norm_root_eq_spectralValuestatement and proof · cited by 1