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while dealing with non-homogeneous equations with constant coefficients I met a following problem. I need an easy way to calculate powers of a superdiagonal matrix (every power up to n-1):

[tex]\mathbb N^{n}_{n} \ni \mathbb M_{n}:=\begin{bmatrix} 0&n-1&0&0&...&0&0&0&0\\0&0&n-2&0&...&0&0&0&0\\0&0&0&n-3&...&0&0&0&0\\...&...&...&...&...&...&...&...&...\\0&0&0&0&...&0&3&0&0\\0&0&0&0&...&0&0&2&0\\0&0&0&0&...&0&0&0&1\\0&0&0&0&...&0&0&0&0 \end{bmatrix}[/tex]

(zeros outside the superdiagonal, an arithmetic progression on the superdiagonal).

Thanks in advance.

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# Powers of a superdiagonal matrix

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