Linear Algebra Done Right · Problem 9C.10

Operators on Real Vector Spaces — Sheldon Axler

Mathematics — Linear Algebra · determinants

Problem

Suppose

V

is a real vector space of odd dimension and

T \in \mathcal{L}(V)

. Without using the minimal polynomial, prove that

T

has an eigenvalue. This result was previously proved without using determinants or the characteristic polynomial---see 5.34.