Theorems · Theorem · linear algebra
Matrix.IsHermitian.splits_charpoly
∀ {𝕜 : Type u_1} [inst : RCLike 𝕜] {n : Type u_2} [inst_1 : Fintype n] {A : Matrix n n 𝕜} [inst_2 : DecidableEq n],
A.IsHermitian → A.charpoly.Splits- Defined in
- Mathlib.Analysis.Matrix.Spectrum
- Cited by
- 2 results in Mathlib
- Foundations
- Depth 264 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.
Cites17
Mathlib declarations this one mentions in its statement or cites explicitly in its proof. Plumbing is filtered out.
- Fintypestatement and proof · cited by 7,736
- Matrixstatement and proof · cited by 4,303
- Finset.univproof · cited by 3,473
- RCLikestatement and proof · cited by 2,829
- Fintype.cardproof · cited by 1,386
- Finset.valproof · cited by 438
- Multiset.cardproof · cited by 375
- RCLike.ofRealproof · cited by 350
- Polynomial.Splitsstatement · cited by 290
- Multiset.map_congrproof · cited by 232
- Matrix.IsHermitianstatement and proof · cited by 126
- Matrix.charpolystatement · cited by 82
Cited by2
Results whose statement or proof uses this declaration.
- Matrix.IsHermitian.det_eq_prod_eigenvaluesproof · cited by 4
- Matrix.IsHermitian.trace_eq_sum_eigenvaluesproof · cited by 0