Theorems · Theorem · linear algebra

Module.End.IsSemisimple.eq_zero_iff_forall_eigenvalue

∀ {K : Type u_3} {V : Type u_4} [inst : Field K] [IsAlgClosed K] [inst_2 : AddCommGroup V] [inst_3 : Module K V]
  [FiniteDimensional K V] {f : Module.End K V}, f.IsSemisimple → (f = 0 ↔ ∀ (μ : K), f.HasEigenvalue μ → μ = 0)

Defined in

Mathlib.LinearAlgebra.Eigenspace.Semisimple

Cited by

0 results in Mathlib

Foundations

Depth 143 from the axioms · uses propext, Classical.choice, Quot.sound

Assumes

FieldIsAlgClosedAddCommGroupModuleFiniteDimensional