Theorems · Theorem · linear algebra
Matrix.det_eq_prod_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.det = B.charpoly.roots.prod- Cited by
- 3 results in Mathlib
- Foundations
- Depth 141 from the axioms · uses propext, Classical.choice, Quot.sound
Around this declaration
Dashed lines are statement dependencies; solid lines are citations in proofs.
Cites21
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
- one_mulproof · cited by 2,841
- IsDomainstatement and proof · cited by 2,196
- mul_assocproof · cited by 1,667
- Polynomial.natDegreeproof · cited by 1,105
- Polynomial.coeffproof · cited by 1,045
- Matrix.detstatement · cited by 665
- Multiset.prodstatement and proof · cited by 528
- one_powproof · cited by 521
- Polynomial.Splitsstatement and proof · cited by 290
Cited by3
Results whose statement or proof uses this declaration.
- Matrix.IsHermitian.det_eq_prod_eigenvaluesproof · cited by 4
- Module.End.det_eq_prod_roots_charpoly_of_splitsproof · cited by 1
- Matrix.det_eq_prod_roots_charpolyproof · cited by 0