Finding eigenvalues and eigenvectors for a 5x5 matrix using the characteristic equation is often tedious and error-prone. Numerical methods such as Newton's method are recommended for approximating eigenvalues when dealing with complex matrices. For those without access to software like Mathematica, MATLAB, or Maple, manual techniques such as the Tschirnhaus transformation and the Rational Root Theorem can be employed to simplify the process. However, these methods still require careful inspection and may lead to errors if not executed properly.
PREREQUISITESStudents and professionals in mathematics, particularly those studying linear algebra, as well as anyone needing to compute eigenvalues and eigenvectors manually for 5x5 matrices.
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?