Re: Jordan canonical form

[Jordi Gutiérrez Hermoso]

On 14 May 2010 12:48, John Swensen <address@hidden> wrote:
> However, it appears that Octave doesn't have the jordan function
> implemented.  Is this correct, or am I missing something?  I
> couldn't find it in either OctaveForge or the main octave sources.
>  Does someone already have an efficient method for finding the
> Jordan canonical form of a matrix?

The problem with the Jordan form, as you're probably aware, is that
it's extremely ill-conditioned numerically. Here's a reference I found
that suggests a method, but I haven't tried to understand it.

     http://portal.acm.org/citation.cfm?id=355912

It's this instability why it's usually not implemented in numerical. I
see that Matlab does have an implementation but only with integers.

Btw, Golub & Van Loan suggest using the stable Schur decomposition
instead in cases where the Jordan form might be desired.

Also, since most matrices are diagonalisable in some precise sense
(e.g. the measure of matrices without a full set of eigenvectors is
zero), it's not so bad that logm assumes diagonalisability.

HTH,
- Jordi G. H.