Theorems · Theorem · linear algebra
LinearMap.charpoly_monic
∀ {R : Type u} {M : Type v} [inst : CommRing R] [inst_1 : AddCommGroup M] [inst_2 : Module R M]
[inst_3 : Module.Free R M] [inst_4 : Module.Finite R M] (f : M →ₗ[R] M), f.charpoly.Monic- Defined in
- Mathlib.LinearAlgebra.Charpoly.Basic
- Cited by
- 6 results in Mathlib
- Foundations
- Depth 115 from the axioms · uses propext, Classical.choice, Quot.sound
Around this declaration
Dashed lines are statement dependencies; solid lines are citations in proofs.
Cites13
Mathlib declarations this one mentions in its statement or cites explicitly in its proof. Plumbing is filtered out.
- DFunLike.coeproof · cited by 62,936
- Modulestatement and proof · cited by 20,661
- RingHom.idstatement and proof · cited by 18,349
- CommRingstatement and proof · cited by 17,173
- AddCommGroupstatement and proof · cited by 12,871
- LinearMapstatement and proof · cited by 10,215
- Module.Finitestatement and proof · cited by 1,032
- Module.Freestatement and proof · cited by 597
- Polynomial.Monicstatement · cited by 461
- LinearMap.toMatrixproof · cited by 180
- Module.Free.chooseBasisproof · cited by 121
- LinearMap.charpolystatement · cited by 67
Cited by6
Results whose statement or proof uses this declaration.
- LinearMap.nilRank_le_natTrailingDegree_charpolyproof · cited by 3
- LinearMap.charpoly_nilpotent_tfaeproof · cited by 2
- LinearMap.isNilRegular_iff_natTrailingDegree_charpoly_eq_nilRankproof · cited by 2
- LinearMap.finrank_maxGenEigenspace_zero_eqproof · cited by 2
- isNilpotent_tensor_residueField_iffproof · cited by 1
- LinearMap.isIntegralproof · cited by 1