The discussion revolves around finding eigenvalues and eigenvectors for a 5x5 matrix, focusing on the challenges associated with using the characteristic equation and the potential for tedious calculations.
There is an ongoing exploration of methods, with some participants suggesting that the problem may be set up for simpler solutions. Others emphasize the difficulty of manual calculations and the potential for errors, while a few offer to assist by providing results if the matrix is shared.
One participant notes the requirement to solve the problem by hand, excluding the use of software, which influences the discussion on feasible methods.
genericusrnme said: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?