Theorems · Theorem · linear algebra
Matrix.IsHermitian.charpoly_eq
∀ {𝕜 : Type u_1} [inst : RCLike 𝕜] {n : Type u_2} [inst_1 : Fintype n] {A : Matrix n n 𝕜} [inst_2 : DecidableEq n]
(hA : A.IsHermitian), A.charpoly = ∏ i, (Polynomial.X - Polynomial.C ↑(hA.eigenvalues i))- Defined in
- Mathlib.Analysis.Matrix.Spectrum
- Cited by
- 2 results in Mathlib
- Foundations
- Depth 262 from the axioms · uses propext, Classical.choice, Quot.sound
- Assumes
- RCLikeFintypeDecidableEq
Around this declaration
Dashed lines are statement dependencies; solid lines are citations in proofs.
Cites26
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
- RingHomstatement · cited by 10,189
- Fintypestatement and proof · cited by 7,736
- Polynomialstatement and proof · cited by 5,681
- Matrixstatement and proof · cited by 4,303
- Finset.univstatement and proof · cited by 3,473
- one_mulproof · cited by 2,841
- RCLikestatement and proof · cited by 2,829
- Finset.prodstatement and proof · cited by 2,356
- mul_assocproof · cited by 1,667
- Polynomial.Xstatement and proof · cited by 1,639
- Polynomial.Cstatement and proof · cited by 1,598
Cited by2
Results whose statement or proof uses this declaration.
- Matrix.IsHermitian.roots_charpoly_eq_eigenvaluesproof · cited by 4
- Matrix.IsHermitian.eigenvalues_eq_eigenvalues_iffproof · cited by 0