Theorems · Theorem · linear algebra
Matrix.charpoly_degree_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.degree = ↑(Fintype.card n)- Cited by
- 4 results in Mathlib
- Foundations
- Depth 113 from the axioms · uses propext, Classical.choice, Quot.sound
Around this declaration
Dashed lines are statement dependencies; solid lines are citations in proofs.
Cites37
Mathlib declarations this one mentions in its statement or cites explicitly in its proof. Plumbing is filtered out.
- DFunLike.coeproof · cited by 62,936
- CommRingstatement and proof · cited by 17,173
- Fintypestatement and proof · cited by 7,736
- Ringproof · cited by 7,463
- Polynomialproof · cited by 5,681
- Finset.sumproof · cited by 5,195
- Matrixstatement and proof · cited by 4,303
- mul_oneproof · cited by 3,885
- Finset.univproof · cited by 3,473
- Nontrivialstatement and proof · cited by 2,416
- Finset.prodproof · cited by 2,356
- Finset.cardproof · cited by 2,327
Cited by4
Results whose statement or proof uses this declaration.
- Matrix.charpoly_natDegree_eq_dimproof · cited by 11
- Matrix.charpoly_monicproof · cited by 9
- charpoly_leftMulMatrixproof · cited by 2
- Matrix.discr_of_card_eq_twoproof · cited by 1