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The maximal determinant and subdeterminants of ±1 matrices

✍ Scribed by Jennifer Seberry; Tianbing Xia; Christos Koukouvinos; Marilena Mitrouli

Publisher
Elsevier Science
Year
2003
Tongue
English
Weight
127 KB
Volume
373
Category
Article
ISSN
0024-3795

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✦ Synopsis

In this paper we study the maximal absolute values of determinants and subdeterminants of ±1 matrices, especially Hadamard matrices. It is conjectured that the determinants of ±1 matrices of order n can have only the values k • p, where p is specified from an appropriate procedure. This conjecture is verified for small values of n. The question of what principal minors can occur in a completely pivoted ±1 matrix is also studied. An algorithm to compute the (nj) × (nj) minors, j = 1, 2, . . . , of Hadamard matrices of order n is presented, and these minors are determined for j = 1, . . . , 4.

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