Theorems · Theorem · linear algebra

Module.End.det_eq_prod_roots_charpoly_of_splits

∀ {K : Type u_3} {V : Type u_4} [inst : Field K] [inst_1 : AddCommGroup V] [inst_2 : Module K V]
  [inst_3 : Module.Finite K V] {f : Module.End K V},
  (LinearMap.charpoly f).Splits → LinearMap.det f = (LinearMap.charpoly f).roots.prod

Defined in: Mathlib.LinearAlgebra.Eigenspace.Charpoly
Cited by: 1 results in Mathlib
Foundations: Depth 142 from the axioms · uses propext, Classical.choice, Quot.sound
Assumes: Field AddCommGroup Module Module.Finite

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DFunLike.coestatement · cited by 62,936
Modulestatement and proof · cited by 20,661
RingHom.idstatement · cited by 18,349
AddCommGroupstatement and proof · cited by 12,871
LinearMapstatement · cited by 10,215
Fieldstatement and proof · cited by 7,404
Polynomialproof · cited by 5,681
MonoidHomstatement · cited by 3,629
Module.Finitestatement and proof · cited by 1,032
Module.Endstatement and proof · cited by 774
Multiset.prodstatement and proof · cited by 528
Polynomial.Splitsstatement and proof · cited by 290

Cited by1

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LinearMap.IsSymmetric.det_eq_prod_eigenvaluesproof · cited by 1