Theorems · Theorem · linear algebra
Matrix.trace_eq_sum_roots_charpoly_of_splits
∀ {n : Type u_1} [inst : Fintype n] [inst_1 : DecidableEq n] {R : Type u_2} [inst_2 : CommRing R] {B : Matrix n n R}
[inst_3 : IsDomain R], B.charpoly.Splits → B.trace = B.charpoly.roots.sum- Cited by
- 3 results in Mathlib
- Foundations
- Depth 140 from the axioms · uses propext, Classical.choice, Quot.sound
Around this declaration
Dashed lines are statement dependencies; solid lines are citations in proofs.
Cites20
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
- IsDomainstatement and proof · cited by 2,196
- IsEmptyproof · cited by 759
- Multiset.sumstatement and proof · cited by 388
- Polynomial.Splitsstatement and proof · cited by 290
- isEmpty_or_nonemptyproof · cited by 269
- Polynomial.rootsstatement and proof · cited by 264
- Matrix.tracestatement · cited by 114
- Matrix.charpolystatement and proof · cited by 82
- neg_eq_iff_eq_negproof · cited by 60
Cited by3
Results whose statement or proof uses this declaration.
- Module.End.trace_eq_sum_roots_charpoly_of_splitsproof · cited by 1
- Matrix.IsHermitian.trace_eq_sum_eigenvaluesproof · cited by 0
- Matrix.trace_eq_sum_roots_charpolyproof · cited by 0