Theorems · Theorem · linear algebra
LinearMap.det_eq_sign_charpoly_coeff
∀ {R : Type u_1} {M : Type u_2} [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),
LinearMap.det f = (-1) ^ Module.finrank R M * f.charpoly.coeff 0- Cited by
- 2 results in Mathlib
- Foundations
- Depth 130 from the axioms · uses propext, Classical.choice, Quot.sound
Around this declaration
Dashed lines are statement dependencies; solid lines are citations in proofs.
Cites26
Mathlib declarations this one mentions in its statement or cites explicitly in its proof. Plumbing is filtered out.
- 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
- Polynomialproof · cited by 5,681
- MonoidHomstatement · cited by 3,629
- one_mulproof · cited by 2,841
- Nontrivialproof · cited by 2,416
- Module.finrankstatement and proof · cited by 1,770
- Polynomial.coeffstatement and proof · cited by 1,045
Cited by2
Results whose statement or proof uses this declaration.
- LinearMap.det_baseChangeproof · cited by 1
- Module.End.hasEigenvalue_iff_isRoot_charpolyproof · cited by 1