Kunze Linear Algebra · Problem 7.3.2

Rational and Jordan Forms

Mathematics — Methods · jordan-form-similarity

Problem

Use the result of Exercise 1 and the Jordan form to prove the following: Let

A

and

B

n \times n

matrices over the field

F

which have the same characteristic polynomial

f = (x - c_1)^{d_1} \cdots (x - c_k)^{d_k}

and the same minimal polynomial. If no

d_i

is greater than 3, then

A

and

B

are similar.