Let R be an n × n upper triangular matrix whose diagonal entries are all distinct. Let Rk denote the leading principal submatrix of R of order k and set U1 = (1).
(a) Use the result from Exercise 11 to derive an algorithm for finding the eigenvectors of R. The matrix U of eigenvectors should be upper triangular with l's on the diagonal.
(b) Show that the algorithm requires approximately n3/6 floating-point multiplications/divisions.