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Diagonalization of Quadratic Forms by Gauss Elimination

Published: 01 January 1966 Publication History

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.

References

[1]
BIRKHOFF, G. AND MACLANE, S., A Survey of Modern Algebra, Macmillan, New York, 1953, p. 270.
[2]
DORN, W. S., "Nonlinear Programming¿A Survey," Management Sci., Vol. 9, 171-208 (1963).
[3]
KUNZ, KAISER S., Numerical Analysis, McGraw-Hill, New York, 1957, pp. 220, 226.
[4]
MOOD, A. M. AND GRAYBILL, F. A., Introduction to the Theory of Statistics, Second Edition, New York, McGraw-Hill, 1963, p. 207.
[5]
WILDE, D. J., Optimum Seeking Methods, Prentice-Hall, Inc., Englewood Cliffs, N. J., 1964, p. 80ff.

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      cover image Management Science
      Management Science  Volume 12, Issue 5
      January 1966
      178 pages

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      INFORMS

      Linthicum, MD, United States

      Publication History

      Published: 01 January 1966

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