, Volume 56, Issue 4, pp 631–636 | Cite as

Kruskal's polynomial for 2×2×2 arrays and a generalization to 2×n×n arrays

  • Jos M. F. ten Berge


A remarkable difference between the concept of rank for matrices and that for three-way arrays has to do with the occurrence of non-maximal rank. The set ofn×n matrices that have a rank less thann has zero volume. Kruskal pointed out that a 2×2×2 array has rank three or less, and that the subsets of those 2×2×2 arrays for which the rank is two or three both have positive volume. These subsets can be distinguished by the roots of a certain polynomial. The present paper generalizes Kruskal's results to 2×n×n arrays. Incidentally, it is shown that twon ×n matrices can be diagonalized simultaneously with positive probability.

Key words

rank three-way arrays PARAFAC CANDECOMP simultaneous diagonalization 


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Copyright information

© The Psychometric Society 1991

Authors and Affiliations

  • Jos M. F. ten Berge
    • 1
  1. 1.University of GroningenThe Netherlands

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