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Canonical forms of some special matrices useful in statistics


In experimental situations wheren two or three level factors are involved andn observations are taken, then theD-optimal first order saturated design is ann ×n matrix with elements ±1 or 0, ±1 with the maximum determinant. Canonical forms are useful for the specification of the non-isomorphicD-optimal designs. In this paper, we study canonical forms such as the Smith normal form, the first, second and the Jordan canonical form ofD-optimal designs. Numerical algorithms for the computation of these forms are described and some numerical examples are also given.

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Correspondence to M. Mitrouli.

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Mitrouli, M., Karcanias, N. & Koukouvinos, C. Canonical forms of some special matrices useful in statistics. Korean J. Comp. & Appl. Math. 4, 63–82 (1997).

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AMS Mathematics Subject Classification

  • 62K05
  • 62K10
  • 15A21

Key words and phrases

  • algorithm
  • D-optimal design
  • canonical form
  • matrix