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where <math>\delta_{ij}</math> is the Kronecker delta symbol.
where <math>\delta_{ij}</math> is the Kronecker delta symbol.
*For example, the 5×5 shift matrices are:
*For example, the 5×5 shift matrices are:
<math>U_5=\begin{pmatrix}
0 & 1 & 0 & 0 & 0 \\
0 & 0 & 1 & 0 & 0 \\
0 & 0 & 0 & 1 & 0 \\
0 & 0 & 0 & 0 & 1 \\
0 & 0 & 0 & 0 & 0
\end{pmatrix}
<math>L_5 = \begin{pmatrix}
0 & 0 & 0 & 0 & 0 \\
1 & 0 & 0 & 0 & 0 \\
0 & 1 & 0 & 0 & 0 \\
0 & 0 & 1 & 0 & 0 \\
0 & 0 & 0 & 0 & 0
\end{pmatrix}
*All shift matrices are nilpotent; an n by n shift matrix S becomes the null matrix when raised to the power of its dimension n.
*All shift matrices are nilpotent; an n by n shift matrix S becomes the null matrix when raised to the power of its dimension n.