Kunze Linear Algebra · Problem 6.2.11

Elementary Canonical Forms

Mathematics — Methods · nilpotent-2x2-complex-matrix

Problem

Let

N

be a

2 \times 2

complex matrix such that

N^2 = 0

. Prove that either

N = 0

N

is similar over

C

\begin{bmatrix} 0 & 0 \\ 1 & 0 \end{bmatrix}.