Journal of applied mathematics & informatics

The Korean Society for Computational and Applied Mathematics (한국전산응용수학회)
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CANONICAL FORMS OF SOME SPECIAL MATRICES USEFUL IN STATISTICS

  • M. Mitrouli (Department of Mathematics University of Athens) ;
  • N. Karcanias (Department of Mathematics, National Technical University of Athens) ;
  • C. Koukouvinos (Department of Mathematics, National Technical University of Athens)
  • Published : 1997.03.01

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Abstract

In experimental situations where n two or three level fac-tors are involoved and n observations are taken then the D-optimal first order saturated design is an $n{\times}n$ matrix with elements $\pm$1 or 0, $\pm$1, with the maximum determinant. Cononical forms are useful for the specification of the non-isomorphic D-optimal designs. In this paper we study canonical forms such as the Smith normal form the first sec-ond and the jordan canonical form of D-optimal designs. Numerical algorithms for the computation of these forms are described and some numerical examples are also given.

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References

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