Linear Algebra Done Right · Problem 8B.3

Operators on Complex Vector Spaces — Sheldon Axler

Mathematics — Linear Algebra · generalized-eigenspaces-similarity

Problem

Suppose

T \in \mathcal{L}(V)

. Suppose

S \in \mathcal{L}(V)

is invertible. Prove that

T

and

S^{-1}TS

have the same eigenvalues with the same multiplicities.