Theorems · Theorem · linear algebra
LinearMap.eval_charpoly
∀ {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) (t : R),
Polynomial.eval t f.charpoly = LinearMap.det ((algebraMap R (M →ₗ[R] M)) t - f)- Defined in
- Mathlib.LinearAlgebra.Charpoly.Basic
- Cited by
- 0 results in Mathlib
- Foundations
- Depth 130 from the axioms · uses propext, Classical.choice, Quot.sound
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- DFunLike.coestatement and proof · 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
- RingHomstatement · cited by 10,189
- Polynomialproof · cited by 5,681
- Algebra.algebraMapstatement and proof · cited by 4,706
- Matrixproof · cited by 4,303
- MonoidHomstatement · cited by 3,629
- Module.Finitestatement and proof · cited by 1,032
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