Theorems · Theorem · commutative algebra
spectralValue_X_sub_C
∀ {R : Type u_1} [inst : SeminormedRing R] [Nontrivial R] (r : R), spectralValue (Polynomial.X - Polynomial.C r) = ‖r‖The polynomial X - r has spectral value ‖ r ‖.
- Cited by
- 1 results in Mathlib
- Foundations
- Depth 196 from the axioms · uses propext, Classical.choice, Quot.sound
- Assumes
- SeminormedRingNontrivial
Around this declaration
Dashed lines are statement dependencies; solid lines are citations in proofs.
Cites27
Mathlib declarations this one mentions in its statement or cites explicitly in its proof. Plumbing is filtered out.
- DFunLike.coestatement and proof · cited by 62,936
- Realstatement and proof · cited by 25,697
- RingHomstatement · cited by 10,189
- Polynomialstatement · cited by 5,681
- Norm.normstatement and proof · cited by 5,413
- Nat.cast_oneproof · cited by 2,501
- Nontrivialstatement and proof · cited by 2,416
- iSupproof · cited by 2,415
- le_reflproof · cited by 2,061
- Nat.cast_zeroproof · cited by 1,870
- Polynomial.Xstatement and proof · cited by 1,639
- Polynomial.Cstatement and proof · cited by 1,598
Cited by1
Results whose statement or proof uses this declaration.
- spectralNorm_extendsproof · cited by 3