Theorems · Theorem · linear algebra
Matrix.charpoly_diagonal
∀ {R : Type u_1} [inst : CommRing R] {n : Type u_4} [inst_1 : DecidableEq n] [inst_2 : Fintype n] (d : n → R),
(Matrix.diagonal d).charpoly = ∏ i, (Polynomial.X - Polynomial.C (d i))- Cited by
- 4 results in Mathlib
- Foundations
- Depth 104 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.
Cites15
Mathlib declarations this one mentions in its statement or cites explicitly in its proof. Plumbing is filtered out.
- DFunLike.coestatement and proof · cited by 62,936
- CommRingstatement and proof · cited by 17,173
- RingHomstatement · cited by 10,189
- Fintypestatement and proof · cited by 7,736
- Polynomialstatement · cited by 5,681
- Finset.univstatement and proof · cited by 3,473
- Finset.prodstatement and proof · cited by 2,356
- Polynomial.Xstatement and proof · cited by 1,639
- Polynomial.Cstatement and proof · cited by 1,598
- Matrix.diagonalstatement and proof · cited by 314
- Matrix.det.congr_simpproof · cited by 91
- Matrix.charpolystatement · cited by 82
Cited by4
Results whose statement or proof uses this declaration.
- LinearMap.IsSymmetric.roots_charpoly_eq_eigenvaluesproof · cited by 4
- Matrix.IsHermitian.charpoly_eqproof · cited by 2
- LinearMap.IsSymmetric.charpoly_eqproof · cited by 1
- Matrix.IsHermitian.charpoly_cfc_eqproof · cited by 0