Theorems · Theorem · number theory
LinearRecurrence.geom_sol_iff_root_charPoly
∀ {R : Type u_1} [inst : CommRing R] (E : LinearRecurrence R) (q : R),
(E.IsSolution fun n => q ^ n) ↔ E.charPoly.IsRoot qThe geometric sequence q^n is a solution of E iff
q is a root of E's characteristic polynomial.
- Defined in
- Mathlib.Algebra.LinearRecurrence
- Cited by
- 2 results in Mathlib
- Foundations
- Depth 99 from the axioms · uses propext, Classical.choice, Quot.sound
- Assumes
- CommRing
Around this declaration
Dashed lines are statement dependencies; solid lines are citations in proofs.
Cites23
Mathlib declarations this one mentions in its statement or cites explicitly in its proof. Plumbing is filtered out.
- DFunLike.coeproof · cited by 62,936
- RingHom.idproof · cited by 18,349
- CommRingstatement and proof · cited by 17,173
- Polynomialproof · cited by 5,681
- Finset.sumproof · cited by 5,195
- Finset.univproof · cited by 3,473
- one_mulproof · cited by 2,841
- zero_addproof · cited by 2,366
- Finset.sum_congrproof · cited by 2,323
- sub_eq_zeroproof · cited by 407
- pow_addproof · cited by 315
- Polynomial.monomialproof · cited by 256
Cited by2
Results whose statement or proof uses this declaration.
- Real.geom_goldenConj_isSol_fibRecproof · cited by 1
- Real.geom_goldenRatio_isSol_fibRecproof · cited by 1