Theorems · Theorem · linear algebra
Matrix.charpoly_sub_diagonal_degree_lt
∀ {R : Type u} [inst : CommRing R] {n : Type v} [inst_1 : DecidableEq n] [inst_2 : Fintype n] (M : Matrix n n R),
(M.charpoly - ∏ i, (Polynomial.X - Polynomial.C (M i i))).degree < ↑(Fintype.card n - 1)- Cited by
- 3 results in Mathlib
- Foundations
- Depth 108 from the axioms · uses propext, Classical.choice, Quot.sound
- Assumes
- CommRingDecidableEqFintype
Around this declaration
Dashed lines are statement dependencies; solid lines are citations in proofs.
Cites53
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
- CommRingstatement and proof · cited by 17,173
- Finsetproof · cited by 13,712
- RingHomstatement · cited by 10,189
- Equivproof · cited by 8,337
- Fintypestatement and proof · cited by 7,736
- Polynomialstatement and proof · cited by 5,681
- Finset.sumproof · cited by 5,195
- Matrixstatement and proof · cited by 4,303
- Finset.univstatement and proof · cited by 3,473
- one_mulproof · cited by 2,841
- Finset.prodstatement and proof · cited by 2,356
Cited by3
Results whose statement or proof uses this declaration.
- Matrix.charpoly_monicproof · cited by 9
- Matrix.charpoly_degree_eq_dimproof · cited by 4
- Matrix.charpoly_coeff_eq_prod_coeff_of_leproof · cited by 1