Matrix Diagonalization

Matrix diagonalization is the process of rewriting a square matrix ( A ) as ( A = PDP^ ), where ( D ) is a diagonal matrix and ( P ) contains the eigenvectors of ( A ). This is only possible if ( A ) has enough linearly independent eigenvectors. Diagonalization simplifies many computations, such as raising ( A ) to a power, because powers of ( D ) are easy to compute.