Editing Nilpotent matrix (section)

===Example 5===
Perhaps some of the most striking examples of nilpotent matrices are <math>n\times n</math> square matrices of the form:

:<math>\begin{bmatrix}
2 & 2 & 2 & \cdots & 1-n \\
n+2 & 1 & 1 & \cdots & -n \\
1 & n+2 & 1 & \cdots & -n \\
1 & 1 & n+2 & \cdots & -n \\
\vdots & \vdots & \vdots & \ddots & \vdots
\end{bmatrix}</math>

The first few of which are:

:<math>\begin{bmatrix}
2 & -1 \\
4 & -2
\end{bmatrix}
\qquad
\begin{bmatrix}
2 & 2 & -2 \\
5 & 1 & -3 \\
1 & 5 & -3
\end{bmatrix}
\qquad
\begin{bmatrix}
2 & 2 & 2 & -3 \\
6 & 1 & 1 & -4 \\
1 & 6 & 1 & -4 \\
1 & 1 & 6 & -4
\end{bmatrix}
\qquad
\begin{bmatrix}
2 & 2 & 2 & 2 & -4 \\
7 & 1 & 1 & 1 & -5 \\
1 & 7 & 1 & 1 & -5 \\
1 & 1 & 7 & 1 & -5 \\
1 & 1 & 1 & 7 & -5
\end{bmatrix}
\qquad
\ldots
</math>

These matrices are nilpotent but there are no zero entries in any powers of them less than the index.<ref name="Mercer2005">{{cite web 
  |url=http://www.idmercer.com/nilpotent.pdf
  |title=Finding "nonobvious" nilpotent matrices
  |last1=Mercer 
  |first1=Idris D.
  |date=31 October 2005 
  |website=idmercer.com
  |publisher=self-published; personal credentials: PhD Mathematics, [[Simon Fraser University]]
  |access-date=5 April 2023
}}</ref>