(load "eigs.lsp")should produce the eigenvalues and eigenvectors of a matrix provided by Simon Blomberg to the xlispstat listserve, and provide you with the two functions eigenvalues and eigenvectors which work in the general matrix case.
Note, however, that other functions provided in these files (e.g. those for calculating Jordan forms) may not work, as they may require other functions which I did not extract from the main Ripon Good Math collection of code.