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Diagonalization of Quadratic Forms by Gauss Elimination

Author

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  • Charles S. Beightler

    (The University of Texas)

  • Douglass J. Wilde

    (Stanford University)

Abstract

The La Grange linear similarity transformation (completing the square) can be used to remove all cross-product terms from a quadratic form. It is shown that the La Grange transformation may be found conveniently by adapting the well-known Gauss elimination procedure for solving linear equations. A simple algorithm for finding the inverse transformation is given. This diagonalization scheme takes much less effort than finding the characteristic roots and vectors. It produces important simplifications in quadratic programming, statistics, and optimization problems.

Suggested Citation

  • Charles S. Beightler & Douglass J. Wilde, 1966. "Diagonalization of Quadratic Forms by Gauss Elimination," Management Science, INFORMS, vol. 12(5), pages 371-379, January.
    • Handle: RePEc:inm:ormnsc:v:12:y:1966:i:5:p:371-379
    DOI: 10.1287/mnsc.12.5.371
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    Cited by:

    1. Berg, Arthur, 2008. "Multivariate lag-windows and group representations," Journal of Multivariate Analysis, Elsevier, vol. 99(10), pages 2479-2496, November.

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