Theorems · Theorem · linear algebra
Matrix.charpoly_natDegree_eq_dim
∀ {R : Type u} [inst : CommRing R] {n : Type v} [inst_1 : DecidableEq n] [inst_2 : Fintype n] [Nontrivial R]
(M : Matrix n n R), M.charpoly.natDegree = Fintype.card n- Cited by
- 11 results in Mathlib
- Foundations
- Depth 114 from the axioms · uses propext, Classical.choice, Quot.sound
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.
- CommRingstatement and proof · cited by 17,173
- Fintypestatement and proof · cited by 7,736
- Matrixstatement and proof · cited by 4,303
- Nontrivialstatement and proof · cited by 2,416
- Fintype.cardstatement · cited by 1,386
- Polynomial.natDegreestatement · cited by 1,105
- Matrix.charpolystatement · cited by 82
- Polynomial.natDegree_eq_of_degree_eq_someproof · cited by 42
- Matrix.charpoly_degree_eq_dimproof · cited by 4
Cited by11
Results whose statement or proof uses this declaration.
- LinearMap.charpoly_natDegreeproof · cited by 3
- Matrix.reverse_charpolyproof · cited by 3
- Matrix.det_eq_prod_roots_charpoly_of_splitsproof · cited by 3
- Matrix.IsHermitian.splits_charpolyproof · cited by 2
- Matrix.charpoly_of_card_eq_twoproof · cited by 2
- Matrix.charpoly.univ_natDegreeproof · cited by 2
- Matrix.trace_eq_neg_charpoly_nextCoeffproof · cited by 1
- Matrix.coeff_charpolyRev_eq_neg_traceproof · cited by 1
- Matrix.isNilpotent_charpoly_sub_pow_of_isNilpotentproof · cited by 1
- Matrix.charpoly_coeff_eq_sum_minorsproof · cited by 0