The maximal determinant and subdeterminants of ±1 matrices

Seberry, J; Xia, T; Koukouvinos, C; Mitrouli, M

dc.contributor.author	Seberry, J	en
dc.contributor.author	Xia, T	en
dc.contributor.author	Koukouvinos, C	en
dc.contributor.author	Mitrouli, M	en
dc.date.accessioned	2014-03-01T02:42:21Z
dc.date.available	2014-03-01T02:42:21Z
dc.date.issued	2003	en
dc.identifier.issn	0024-3795	en
dc.identifier.uri	https://dspace.lib.ntua.gr/xmlui/handle/123456789/30959
dc.subject	Completely pivoted	en
dc.subject	Hadamard matrices	en
dc.subject	Minors	en
dc.subject	Subdeterminants	en
dc.subject.classification	Mathematics, Applied	en
dc.subject.other	Algorithms	en
dc.subject.other	Quadratic programming	en
dc.subject.other	Vectors	en
dc.subject.other	Hadamard matrices	en
dc.subject.other	Matrix algebra	en
dc.title	The maximal determinant and subdeterminants of ±1 matrices	en
heal.type	conferenceItem	en
heal.identifier.primary	10.1016/S0024-3795(03)00584-6	en
heal.identifier.secondary	http://dx.doi.org/10.1016/S0024-3795(03)00584-6	en
heal.language	English	en
heal.publicationDate	2003	en
heal.abstract	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) x (n - j) minors, j = 1, 2, . . . ,of Hadamard matrices of order n is presented, and these minors are determined for j = 1, . . . , 4. (C) 2003 Elsevier Inc. All rights reserved.	en
heal.publisher	ELSEVIER SCIENCE INC	en
heal.journalName	Linear Algebra and Its Applications	en
dc.identifier.doi	10.1016/S0024-3795(03)00584-6	en
dc.identifier.isi	ISI:000185778400021	en
dc.identifier.volume	373	en
dc.identifier.issue	SUPPL.	en
dc.identifier.spage	297	en
dc.identifier.epage	310	en