Optimally rotated vectors (Q1415241)

A Lagrange multiplier technique is used to compute the vectors which undergo maximum or minimum rotation by a matrix on the field of real numbers. The optimization problems are converted into systems of nonlinear equations. However, these systems are hard to be solved algebraically even in the case of \(2\times 2\) matrices. Therefore, numerical methods are considered. Obviously, more work is needed to be done.