International Journal of Mathematics and Mathematical Sciences
Volume 2003 (2003), Issue 63, Pages 4015-4023

Optimally rotated vectors

Morteza Seddighin

Division of Natural Science and Mathematics, Indiana University East, Richmond 47374, IN, USA

Received 5 August 2002

Copyright © 2003 Morteza Seddighin. This is an open access article distributed under the Creative Commons Attribution License, which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited.


We study vectors which undergo maximum or minimum rotation by a matrix on the field of real numbers. The cosine of the angle between a maximally rotated vector and its image under the matrix is called the cosine or antieigenvalue of the matrix and has important applications in numerical methods. Using Lagrange multiplier technique, we obtain systems of nonlinear equations which represent these optimization problems. Furthermore, we solve these systems symbolically and numerically.