The maximal determinant and subdeterminants of ±1 matrices

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...

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Bibliographic Details
Published in:Linear algebra and its applications 2003-11, Vol.373, p.297-310
Main Authors: Seberry, Jennifer, Xia, Tianbing, Koukouvinos, Christos, Mitrouli, Marilena
Format: Article
Language:English
Subjects:
Applied sciences
Artificial intelligence
Completely pivoted
Computer science
control theory
systems
Connectionism. Neural networks
Exact sciences and technology
Hadamard matrices
Minors
Subdeterminants
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Summary: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 ( n− j)×( n− j) minors, j=1,2,…, of Hadamard matrices of order n is presented, and these minors are determined for j=1,…,4.
ISSN:0024-3795
1873-1856
DOI:10.1016/S0024-3795(03)00584-6