Solved: Let R be an n n upper triangular matrix whose diagonal entries are all distinct

Chapter 7, Problem 13

(choose chapter or problem)

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 12 to derive an algorithm for finding the eigenvectors of R. The matrix U of eigenvectors should be upper triangular with 1s on the diagonal. (b) Show that the algorithm requires approximately n3 6 floating-point multiplications/ divisions.