- #1
protaktyn
- 2
- 0
Hello,
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.
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.