Linear Algebra Done Right · Problem 8B.4

Operators on Complex Vector Spaces — Sheldon Axler

Mathematics — Linear Algebra · generalized-eigenspaces

Problem

Suppose

\dim V \geq 2

and

T \in \mathcal{L}(V)

is such that

\operatorname{null} T^{\dim V - 2} \neq \operatorname{null} T^{\dim V - 1}

. Prove that

T

has at most two distinct eigenvalues.