Apply the technique of Lagrange multipliers to the problem of maximizing xT Ax subject to xTx = 1. Show how it relates to the matrix eigenproblem. For a symmetric matrix of order n, how much work is...

Apply the technique of Lagrange multipliers to the problem of maximizing xT Ax subject to xTx = 1. Show how it relates to the matrix eigenproblem.

For a symmetric matrix of order n, how much work is required to reduce it to tridiagonal form through the use of similarity transformations?