Theorems · Theorem · commutative algebra
spectralNorm_zero_lt
∀ {K : Type u_2} [inst : NormedField K] {L : Type u_3} [inst_1 : Field L] [inst_2 : Algebra K L] {y : L},
y ≠ 0 → IsAlgebraic K y → 0 < spectralNorm K L yspectralNorm K L y is positive if y ≠ 0.
- Cited by
- 3 results in Mathlib
- Foundations
- Depth 198 from the axioms · uses propext, Classical.choice, Quot.sound
- Assumes
- NormedFieldFieldAlgebra
Around this declaration
Dashed lines are statement dependencies; solid lines are citations in proofs.
Cites21
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
- Algebrastatement and proof · cited by 11,388
- Fieldstatement and proof · cited by 7,404
- Polynomialproof · cited by 5,681
- Polynomial.Xproof · cited by 1,639
- Polynomial.natDegreeproof · cited by 1,105
- NormedFieldstatement and proof · cited by 1,084
- Polynomial.coeffproof · cited by 1,045
- minpolyproof · cited by 439
- lt_of_le_of_neproof · cited by 230
- ne_of_ltproof · cited by 203
- IsAlgebraicstatement and proof · cited by 163
Cited by3
Results whose statement or proof uses this declaration.
- eq_zero_of_map_spectralNorm_eq_zeroproof · cited by 0
- algNormFromConst_defstatement · cited by 0
- spectralAlgNorm_mulproof · cited by 0