Ackbeet , oh yes , i am actually talking about the degenerate eigenvalues ,

not the degenerate eigenvectors..

after checking with the problem i was having , i am able to get the set of

common eigenvectors for the two commuting hermitian matrices having degenerate

eigenvalues. i needed to choose the indeterminate constants properly so that

the set of eigenvectors matched.

but the theorem i quoted doesn't say anything about the hermitian nature of the

matrices. so is it more general theorem , valid for non hermitian commuting matrices as well ?