Theorems · Theorem · linear algebra
Matrix.charpoly_monic
∀ {R : Type u} [inst : CommRing R] {n : Type v} [inst_1 : DecidableEq n] [inst_2 : Fintype n] (M : Matrix n n R),
M.charpoly.Monic- Cited by
- 9 results in Mathlib
- Foundations
- Depth 114 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.
Cites26
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
- Polynomialproof · cited by 5,681
- Matrixstatement and proof · cited by 4,303
- Finset.univproof · cited by 3,473
- Nontrivialproof · cited by 2,416
- Finset.prodproof · cited by 2,356
- Polynomial.Xproof · cited by 1,639
- Polynomial.Cproof · cited by 1,598
- WithBotproof · cited by 1,498
- Fintype.cardproof · cited by 1,386
Cited by9
Results whose statement or proof uses this declaration.
- LinearMap.charpoly_monicproof · cited by 6
- Matrix.trace_eq_sum_roots_charpoly_of_splitsproof · cited by 3
- Matrix.det_eq_prod_roots_charpoly_of_splitsproof · cited by 3
- Matrix.charpoly.univ_monicproof · cited by 3
- charpoly_leftMulMatrixproof · cited by 2
- Matrix.charpoly_of_card_eq_twoproof · cited by 2
- Matrix.det_detproof · cited by 1
- Matrix.isIntegralproof · cited by 0