Theorems · Theorem · commutative algebra
spectralNorm_extends
∀ {K : Type u_2} [inst : NormedField K] {L : Type u_3} [inst_1 : Field L] [inst_2 : Algebra K L] (k : K),
spectralNorm K L ((algebraMap K L) k) = ‖k‖The spectral norm extends the norm on K.
- Cited by
- 3 results in Mathlib
- Foundations
- Depth 197 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.
Cites13
Mathlib declarations this one mentions in its statement or cites explicitly in its proof. Plumbing is filtered out.
- DFunLike.coestatement · cited by 62,936
- Realstatement · cited by 25,697
- Algebrastatement and proof · cited by 11,388
- RingHomstatement · cited by 10,189
- Fieldstatement and proof · cited by 7,404
- Norm.normstatement and proof · cited by 5,413
- Algebra.algebraMapstatement and proof · cited by 4,706
- NormedFieldstatement and proof · cited by 1,084
- RingHom.injectiveproof · cited by 187
- spectralNormstatement · cited by 31
- spectralValueproof · cited by 13
- minpoly.eq_X_sub_C_of_algebraMap_injproof · cited by 4
Cited by3
Results whose statement or proof uses this declaration.
- spectralNorm_oneproof · cited by 1
- spectralNorm.spectralNorm_eq_norm_coeff_zero_rpowproof · cited by 0
- spectralAlgNorm_extendsproof · cited by 0