oliver

01-07-2005, 08:46 AM

Dear All,

I like to calculate the eigenvalues and eigenvectors of a hermitian matrix.

In section 11.4 of the NR it is suggested to convert it into a real symmetric matrix, and then to just choose one eigenvalue and eigenvector from each pair. This sounds easy a first, but has an obvious problem in the case of degeneracies. That is, if an eigenvalue is e.g. twofold degenerate, then this eigenvalue will appear 4 times. It is then not apparent any more which of the eigenvectors correspond to a pair.

Has anyone an idea of how to identify the eigenvectors of a pair?

I first thougt that one can do this by searching for the vector (-v,u), corresponding to (u,v), but I can't see why this should work in general.

Thanks in advance,

Oliver

I like to calculate the eigenvalues and eigenvectors of a hermitian matrix.

In section 11.4 of the NR it is suggested to convert it into a real symmetric matrix, and then to just choose one eigenvalue and eigenvector from each pair. This sounds easy a first, but has an obvious problem in the case of degeneracies. That is, if an eigenvalue is e.g. twofold degenerate, then this eigenvalue will appear 4 times. It is then not apparent any more which of the eigenvectors correspond to a pair.

Has anyone an idea of how to identify the eigenvectors of a pair?

I first thougt that one can do this by searching for the vector (-v,u), corresponding to (u,v), but I can't see why this should work in general.

Thanks in advance,

Oliver