Kunze Linear Algebra · Problem 7.1.1

Rational and Jordan Forms

Mathematics — Methods · cyclic-subspaces

Problem

Let

T

be a linear operator on

F^2

. Prove that any non-zero vector which is not a characteristic vector for

T

is a cyclic vector for

T

. Hence, prove that either

T

has a cyclic vector or

T

is a scalar multiple of the identity operator.