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Optimally rotated vectors

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  • Morteza Seddighin

Abstract

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.

Suggested Citation

  • Morteza Seddighin, 2003. "Optimally rotated vectors," International Journal of Mathematics and Mathematical Sciences, Hindawi, vol. 2003, pages 1-9, January.
    • Handle: RePEc:hin:jijmms:962457
    DOI: 10.1155/S0161171203208334
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