Theorems · Definition · linear algebra
Matrix.IsHermitian.eigenvalues
{𝕜 : Type u_1} →
[inst : RCLike 𝕜] → {n : Type u_2} → [Fintype n] → {A : Matrix n n 𝕜} → [DecidableEq n] → A.IsHermitian → n → ℝThe eigenvalues of a Hermitian matrix, reusing the index n of the matrix entries.
- Defined in
- Mathlib.Analysis.Matrix.Spectrum
- Cited by
- 34 results in Mathlib
- Foundations
- Depth 256 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.
Cites9
Mathlib declarations this one mentions in its statement or cites explicitly in its proof. Plumbing is filtered out.
- DFunLike.coeproof · cited by 62,936
- Realstatement · cited by 25,697
- Fintypestatement and proof · cited by 7,736
- Matrixstatement and proof · cited by 4,303
- Equiv.symmproof · cited by 3,681
- RCLikestatement and proof · cited by 2,829
- Matrix.IsHermitianstatement and proof · cited by 126
- Fintype.equivOfCardEqproof · cited by 23
- Matrix.IsHermitian.eigenvalues₀proof · cited by 5
Cited by36
Results whose statement or proof uses this declaration.
- Matrix.IsHermitian.spectral_theoremstatement · cited by 10
- Matrix.IsHermitian.cfcAuxproof · cited by 6
- Matrix.PosSemidef.eigenvalues_nonnegstatement · cited by 6
- Matrix.IsHermitian.roots_charpoly_eq_eigenvaluesstatement and proof · cited by 4
- Matrix.IsHermitian.det_eq_prod_eigenvaluesstatement and proof · cited by 4
- Matrix.IsHermitian.cfc_eqproof · cited by 3
- Matrix.IsHermitian.mulVec_eigenvectorBasisstatement and proof · cited by 3
- Matrix.IsHermitian.posSemidef_iff_eigenvalues_nonnegstatement and proof · cited by 2
- Matrix.IsHermitian.splits_charpolyproof · cited by 2
- Matrix.IsHermitian.cfcproof · cited by 2
- Matrix.IsHermitian.cfcAux_applystatement · cited by 2
- Matrix.IsHermitian.cfcAux_idproof · cited by 2