Math Is Fun Forum

to answer your question d: the best way to find out whether two matrices A and B are similar or not is by finding the modal matrix P that relates both matrices: B = inverse(P)*A*P. If the modal matrix P exist, you can be sure that A and B are similar. Modal matrix can be obtained from the concatenation of eigenvectors of matrix A. I found out Kardi Teknomo's tutorial (please Google it) on Linear Algebra give a reasonable good explanation with worked out numerical examples.

You can solve the above problem easily using Computer Algebra System like Mathematica or Maple, or using the free one like Maxima (again you can Google it since the forum does not allow me to post link).