Diagonalization of Quadratic Forms by Gauss Elimination
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.
Year of publication: |
1966
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Authors: | Beightler, Charles S. ; Wilde, Douglass J. |
Published in: |
Management Science. - Institute for Operations Research and the Management Sciences - INFORMS, ISSN 0025-1909. - Vol. 12.1966, 5, p. 371-379
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Publisher: |
Institute for Operations Research and the Management Sciences - INFORMS |
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