# Re: R-alpha: matrix exponentiation

Thomas Lumley (thomas@biostat.washington.edu)
Wed, 20 Nov 1996 09:14:33 -0800 (PST)

```Date: Wed, 20 Nov 1996 09:14:33 -0800 (PST)
From: Thomas Lumley <thomas@biostat.washington.edu>
To: Jim Lindsey <jlindsey@luc.ac.be>
Subject: Re: R-alpha: matrix exponentiation

On Wed, 20 Nov 1996, Jim Lindsey wrote:

> 3.Here is a matrix exponentiation function for anyone working on
>   stochastic processes. If anyone knows a better algorithm than brute
>   force, please let me know. Jim

There is a *much* better algorithm, at least for symmetric matrices.  Get
the eigendecomposition and work with that
(this function needs argument checking, of course)
mexp2<-function (mat, n)
{
ei <- eigen(mat)
t(ei\$vectors) %*% diag(exp(ei\$values)) %*% ei\$vectors
}

I think that you can do something similar with the singular value
decomposition for general square matrices but I would have to look it up.

thomas lumley
UW biostatistics
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```