Theorems · Theorem · linear algebra
Matrix.trace_eq_neg_charpoly_coeff
∀ {R : Type u} [inst : CommRing R] {n : Type v} [inst_1 : DecidableEq n] [inst_2 : Fintype n] [Nonempty n]
(M : Matrix n n R), M.trace = -M.charpoly.coeff (Fintype.card n - 1)See also Matrix.coeff_charpolyRev_eq_neg_trace.
- Cited by
- 5 results in Mathlib
- Foundations
- Depth 117 from the axioms · uses propext, Classical.choice, Quot.sound
Around this declaration
Dashed lines are statement dependencies; solid lines are citations in proofs.
Cites18
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
- Finset.sumproof · cited by 5,195
- Matrixstatement and proof · cited by 4,303
- Finset.univproof · cited by 3,473
- Finset.prodproof · cited by 2,356
- Polynomial.Xproof · cited by 1,639
- Polynomial.Cproof · cited by 1,598
- le_rflproof · cited by 1,558
- Fintype.cardstatement · cited by 1,386
- Polynomial.coeffstatement and proof · cited by 1,045
Cited by5
Results whose statement or proof uses this declaration.
- PowerBasis.trace_gen_eq_nextCoeff_minpolyproof · cited by 2
- Matrix.charpoly_of_card_eq_twoproof · cited by 2
- Matrix.trace_eq_neg_charpoly_nextCoeffproof · cited by 1
- FiniteField.trace_pow_cardproof · cited by 1
- Matrix.coeff_charpolyRev_eq_neg_traceproof · cited by 1