Theorems · Theorem · linear algebra

LinearMap.polyCharpoly_ne_zero

∀ {R : Type u_1} {L : Type u_2} {M : Type u_3} {ι : Type u_5} [inst : CommRing R] [inst_1 : AddCommGroup L]
  [inst_2 : Module R L] [inst_3 : AddCommGroup M] [inst_4 : Module R M] (φ : L →ₗ[R] Module.End R M)
  [inst_5 : Fintype ι] [inst_6 : DecidableEq ι] [inst_7 : Module.Free R M] [inst_8 : Module.Finite R M]
  (b : Module.Basis ι R L) [Nontrivial R], φ.polyCharpoly b ≠ 0

Defined in: Mathlib.Algebra.Module.LinearMap.Polynomial
Cited by: 1 results in Mathlib
Foundations: Depth 117 from the axioms · uses propext, Classical.choice, Quot.sound
Assumes: CommRing AddCommGroup Module AddCommGroup Module Fintype DecidableEq Module.Free Module.Finite Nontrivial

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Mathlib declarations this one mentions in its statement or cites explicitly in its proof. Plumbing is filtered out.

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
Fintypestatement and proof · cited by 7,736
Polynomialstatement · cited by 5,681
Finsuppstatement · cited by 5,255
Nontrivialstatement and proof · cited by 2,416
MvPolynomialstatement · cited by 2,140
Module.Basisstatement and proof · cited by 1,477
Module.Finitestatement and proof · cited by 1,032

Cited by1

Results whose statement or proof uses this declaration.

LinearMap.polyCharpoly_coeff_nilRankAux_ne_zeroproof · cited by 2