16.-Linear-Algebra-by-Kenneth-Hoffman · Problem 7.2.11

The Rational and Jordan Forms

Mathematics — Linear Algebra · similarity-of-matrices

Problem

Prove that if

A

and

B

are

3 \times 3

matrices over the field

F

, a necessary and sufficient condition that

A

and

B

be similar over

F

is that they have the same characteristic polynomial and the same minimal polynomial. Give an example which shows that this is false for

4 \times 4

matrices.