Theorems · Theorem · linear algebra

LinearMap.charpoly_zero

∀ {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] [StrongRankCondition R],
  LinearMap.charpoly 0 = Polynomial.X ^ Module.finrank R M

Defined in: Mathlib.LinearAlgebra.Charpoly.Basic
Cited by: 0 results in Mathlib
Foundations: Depth 113 from the axioms · uses propext, Classical.choice, Quot.sound
Assumes: CommRing AddCommGroup Module Module.Free Module.Finite StrongRankCondition

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DFunLike.coeproof · cited by 62,936
Modulestatement and proof · cited by 20,661
RingHom.idstatement · cited by 18,349
CommRingstatement and proof · cited by 17,173
AddCommGroupstatement and proof · cited by 12,871
LinearMapstatement · cited by 10,215
Polynomialstatement · cited by 5,681
Module.finrankstatement · cited by 1,770
Polynomial.Xstatement and proof · cited by 1,639
map_zeroproof · cited by 1,614
Fintype.cardproof · cited by 1,386
Module.Finitestatement and proof · cited by 1,032

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