Hello,(adsbygoogle = window.adsbygoogle || []).push({});

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.

**Physics Forums | Science Articles, Homework Help, Discussion**

Dismiss Notice

Join Physics Forums Today!

The friendliest, high quality science and math community on the planet! Everyone who loves science is here!

The friendliest, high quality science and math community on the planet! Everyone who loves science is here!

# Powers of a superdiagonal matrix

**Physics Forums | Science Articles, Homework Help, Discussion**