An iterative procedure to compute the modal matrix of eigenvectors

The matrix C−1 An, where A is a square non-singular matrix with real coefficients, n a positive integer, and C the triangular matrix resulting from the Cholesky factorization An(An)T = CCT, is orthogonal and a convergent to the orthogonal matrix X for which XAX−1 is triangular. This matrix can be computed to any desired degree of precision by iteration. For symmetric A, (A = AT), X is the modal matrix (matrix of unit eigenvectors) and the convergence is considerably accelerated.