Kunze Linear Algebra · Problem 6.3.11

Elementary Canonical Forms

Mathematics — Methods · ab-ba-characteristic-minimal-polynomial

Problem

Let

A

and

B

n \times n

matrices over the field

F

. According to Exercise 9 of Section 6.1, the matrices

AB

and

BA

have the same characteristic values. Do they have the same characteristic polynomial? Do they have the same minimal polynomial?