Theorems · Theorem · linear algebra

Module.End.exists_eigenvalue

∀ {K : Type u_1} {V : Type u_2} [inst : Field K] [inst_1 : AddCommGroup V] [inst_2 : Module K V] [IsAlgClosed K]
  [FiniteDimensional K V] [Nontrivial V] (f : Module.End K V), ∃ c, f.HasEigenvalue c

In finite dimensions, over an algebraically closed field, every linear endomorphism has an eigenvalue.

Defined in

Mathlib.LinearAlgebra.Eigenspace.Triangularizable

Cited by

1 results in Mathlib

Foundations

Depth 140 from the axioms · uses propext, Classical.choice, Quot.sound

Assumes

FieldAddCommGroupModuleIsAlgClosedFiniteDimensionalNontrivial