Theorems · Theorem · linear algebra
Matrix.coeff_charpolyRev_eq_neg_trace
∀ {R : Type u} [inst : CommRing R] {n : Type v} [inst_1 : DecidableEq n] [inst_2 : Fintype n] (M : Matrix n n R),
M.charpolyRev.coeff 1 = -M.trace- Cited by
- 1 results in Mathlib
- Foundations
- Depth 118 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.
Cites25
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
- Matrixstatement and proof · cited by 4,303
- Nontrivialproof · cited by 2,416
- Polynomial.Xproof · cited by 1,639
- Polynomial.Cproof · cited by 1,598
- Fintype.cardproof · cited by 1,386
- Polynomial.natDegreeproof · cited by 1,105
- Polynomial.coeffstatement and proof · cited by 1,045
- neg_negproof · cited by 960
- IsEmptyproof · cited by 759
Cited by1
Results whose statement or proof uses this declaration.
- Matrix.isNilpotent_trace_of_isNilpotentproof · cited by 3