Open Access. Powered by Scholars. Published by Universities.®
Physical Sciences and Mathematics Commons™
Open Access. Powered by Scholars. Published by Universities.®
Articles 1 - 3 of 3
Full-Text Articles in Physical Sciences and Mathematics
On Circulant Best Matrices And Their Applications, S. Georgiou, C. Koukouvinos, Jennifer Seberry
On Circulant Best Matrices And Their Applications, S. Georgiou, C. Koukouvinos, Jennifer Seberry
Faculty of Informatics - Papers (Archive)
Call four type 1(1,-1) matrices, x1,x2,x3,x4; of the same group of order m (odd) with the properties (i) (Xi-I)T = -(Xi-I), i=1,2,3, (ii)XT4 = X4 and the diagonal elements are positive, (iii) XiXj = XjXi and (iv) X1XT1 + X2XT2+X3XT3 +X4XT4 = 4mIm, best matrices. We use a computer to give, for the first time, all inequivalent best matrices …
An Algorithm To Find Formulae And Values Of Minors For Hadamard Matrices, C. Koukouvinos, M. Mitrouli, Jennifer Seberry
An Algorithm To Find Formulae And Values Of Minors For Hadamard Matrices, C. Koukouvinos, M. Mitrouli, Jennifer Seberry
Faculty of Informatics - Papers (Archive)
We give an algorithm to obtain formulae and values for minors of Hadamard matrices. One step in our algorithm allows the (n – j) x (n – j) minors of an Hadamard matrix to be given in terms of the minors of a 2j-1 x 2j-1 matrix. In particular we illustrate our algorithm by finding explicitly all the (n – 4) x (n – 4) minors of an Hadamard matrix.
On The Complete Pivoting Conjecture For Hadamard Matrices Of Small Orders, C. Koukouvinos, M. Mitrouli, Jennifer Seberry
On The Complete Pivoting Conjecture For Hadamard Matrices Of Small Orders, C. Koukouvinos, M. Mitrouli, Jennifer Seberry
Faculty of Informatics - Papers (Archive)
In this paper we study explicitly the pivot structure of Hadamard matrices of small orders 16, 20 and 32. An algorithm computing the (n — j) x (n — j) minors of Hadamard matrices is presented and its implementation for n = 12 is described. Analytical tables summarizing the pivot patterns attained are given.