Optimally rotated vectors. (English) Zbl 1040.65037

Seddighin, Morteza

Int. J. Math. Math. Sci. 2003, No. 63, 4015-4023 (2003).

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.

Reviewer: Liu Xinguo (Qingdao)

MSC:

65F30

Other matrix algorithms (MSC2010)

Keywords:

optimally rotated vector; Lagrange multiplier; systems of nonlinear equations