Theorems · Theorem · commutative algebra
spectralNorm_nonneg
∀ {K : Type u_2} [inst : NormedField K] {L : Type u_3} [inst_1 : Field L] [inst_2 : Algebra K L] (y : L),
0 ≤ spectralNorm K L yspectralNorm K L y is nonnegative.
- Cited by
- 2 results in Mathlib
- Foundations
- Depth 196 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.
Cites9
Mathlib declarations this one mentions in its statement or cites explicitly in its proof. Plumbing is filtered out.
- Realstatement · cited by 25,697
- Algebrastatement and proof · cited by 11,388
- Fieldstatement and proof · cited by 7,404
- NormedFieldstatement and proof · cited by 1,084
- minpolyproof · cited by 439
- spectralNormstatement · cited by 31
- le_ciSup_of_leproof · cited by 22
- spectralValueTerms_bddAboveproof · cited by 3
- spectralValueTerms_nonnegproof · cited by 3
Cited by2
Results whose statement or proof uses this declaration.
- spectralNorm_zero_ltproof · cited by 3
- spectralNorm.spectralNorm_eq_norm_coeff_zero_rpowproof · cited by 0