Numerical comutation of eigensystems?



Hello,

is there a Maxima function for the numerical computation of eigenystems? 
The symbolic methods used in the eigenvectors(..) and eigenvalues(..) 
functions (as well as in related functions such as jordan or modematrix) 
of course usually fail for matrices of order greater than 4.

As for the eigenvalues, I could of course compute allroots of the 
charpoly, but this doesn't help much for eigenvectors, since approximate 
  eigenvalues result in a trivial nullspace.

Kind regards

Uwe