Kunze Linear Algebra · Problem 7.3.11

Rational and Jordan Forms

Mathematics — Methods · nilpotent-matrices-similarity

Problem

Let

N_1

and

N_2

6 \times 6

nilpotent matrices over the field

F

. Suppose that

N_1

and

N_2

have the same minimal polynomial and the same nullity. Prove that

N_1

and

N_2

are similar. Show that this is not true for

7 \times 7

nilpotent matrices.