I got a 5x5 matrix, if use characteristic equation to find the eigenvalues and eigenvectors are very tedious and trouble, so got any method which are easy to calculate?
unless you've got a nice matrix (read diagonal) you're going to have to use some tricks, if you're lucky you can use the tschirnhaus transformation but most likely you'll have to resort to numerical approximations for the eigenvalues (newtons method or something) then you'll have to churn through to find the nullspace manually
it's pretty tedious work and chances are that you'd end up making an error doing it anyway..
you could just use mathematica or matlab, that'd be easier
if you don't have any of those, post your matrix and I'll give you the results, if you want?