if A is a square matrix, and A' = B-1AB is its similarity transform (with a non-singular similarity transformation matrix B), then the eigenvalues of A and A' are supposed to be the same. I can verify this for all most all cases of A. But, it doesn't seem to work, when the eigen values of A are all zero. For example, it doesn't work when A = [0 1 0;0 0 0; 1 0 0]. Yet I can't see why, it shouldn't work. from http://mathworld.wolfram.com/SimilarityTransformation.html the eigen values of A' is given as a solution of =0 = 0 = 0 = 0 = 0 =0 which is the solution for eigen values of A.