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Articles 1 - 3 of 3
Full-Text Articles in Physical Sciences and Mathematics
Values Of Minors Of (1,-1) Incidence Matrices Of Sbibds And Their Application To The Growth Problem, C Koukouvinos, M Mitrouli, Jennifer Seberry
Values Of Minors Of (1,-1) Incidence Matrices Of Sbibds And Their Application To The Growth Problem, C Koukouvinos, M Mitrouli, Jennifer Seberry
Faculty of Informatics - Papers (Archive)
We obtain explicit formulae for the values of the v j minors, j = 0, 1,2 of (1, -1) incidence matrices of SBIBD(v, k, λ). This allows us to obtain explicit information on the growth problem for families of matrices with moderate growth. An open problem remains to establish whether the (1, -1) CP incidence matrices of SBIBD(v, k, λ), can have growth greater than v for families other than Hadamard families.
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.