Theorems · Theorem · linear algebra
Matrix.trace_eq_neg_charpoly_nextCoeff
∀ {R : Type u} [inst : CommRing R] {n : Type v} [inst_1 : DecidableEq n] [inst_2 : Fintype n] (M : Matrix n n R),
M.trace = -M.charpoly.nextCoeff- 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.
Cites18
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
- Nontrivialproof · cited by 2,416
- Fintype.cardproof · cited by 1,386
- Polynomial.natDegreeproof · cited by 1,105
- Polynomial.coeffproof · cited by 1,045
- IsEmptyproof · cited by 759
- neg_zeroproof · cited by 542
- isEmpty_or_nonemptyproof · cited by 269
- Matrix.tracestatement and proof · cited by 114
- Matrix.charpolystatement and proof · cited by 82
Cited by1
Results whose statement or proof uses this declaration.
- Matrix.trace_eq_sum_roots_charpoly_of_splitsproof · cited by 3