Theorems · Theorem · linear algebra
Matrix.finite_spectrum
∀ {n : Type u_1} {R : Type u_2} [inst : Field R] [inst_1 : Fintype n] [inst_2 : DecidableEq n] (A : Matrix n n R),
(spectrum R A).FiniteAn n x n matrix over a field has a finite spectrum.
- Defined in
- Mathlib.LinearAlgebra.Eigenspace.Minpoly
- Cited by
- 1 results in Mathlib
- Foundations
- Depth 139 from the axioms · uses propext, Classical.choice, Quot.sound
- Assumes
- FieldFintypeDecidableEq
Around this declaration
Dashed lines are statement dependencies; solid lines are citations in proofs.
Cites11
Mathlib declarations this one mentions in its statement or cites explicitly in its proof. Plumbing is filtered out.
- DFunLike.coeproof · cited by 62,936
- Setproof · cited by 53,352
- Fintypestatement and proof · cited by 7,736
- Fieldstatement and proof · cited by 7,404
- Matrixstatement and proof · cited by 4,303
- Set.Finitestatement and proof · cited by 1,814
- spectrumstatement · cited by 510
- Pi.basisFunproof · cited by 78
- Matrix.toLinAlgEquivproof · cited by 13
- AlgEquiv.spectrum_eqproof · cited by 9
- Module.End.finite_spectrumproof · cited by 1
Cited by1
Results whose statement or proof uses this declaration.
- Matrix.finite_real_spectrumproof · cited by 0