I believe mathematica uses some techniques beyond our book. According to the text book it is not possible to solve eigenvalues of which the matrix has not completely eigenvectors, or of those matrix has cluster eigenvalues and multiple matrix yet not symmetric. How does mathematica solve that? On mathematica book they say they use interpolation for the characteristic polynomials, yet there are no thesis pertaining to this. I want to know the algorithm, how can I do so?