1
$\begingroup$

I have a 4x4 matrix $M$ and a 4-length vector $V$, and I want to find $M^k\times V$ for very large $k$. Even if I did exponentiation by squaring, there would be way too many steps involved in terms of halving $k$ simply because it is so large. Is there a better way?

1 Answers 1

5

Write $M = PJP^{-1}$ where $J$ is in Jordan normal form. Then $M^k = PJ^kP^{-1}$, and powers of Jordan normal form matrices are much easier to compute.

  • 0
    @user51819 No, not really. As I said earlier, squaring is easy, anything else is harder because you need to square first anyway.2012-12-09