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Full-Text Articles in Physical Sciences and Mathematics
On The Growth Problem For Skew And Symmetric Conference Matrices, C. Kravvaritis, M. Mitrouli, Jennifer Seberry
On The Growth Problem For Skew And Symmetric Conference Matrices, C. Kravvaritis, M. Mitrouli, Jennifer Seberry
Faculty of Informatics - Papers (Archive)
C. Koukouvinos, M. Mitrouli and Jennifer Seberry, in "Growth in Gaussian elimination for weighing matrices, W (n, n — 1)", Linear Algebra and its Appl., 306 (2000), 189-202, conjectured that the growth factor for Gaussian elimination of any completely pivoted weighing matrix of order n and weight n— 1 is n— 1 and that the first and last few pivots are (1,2,2,3 or 4, ..., n–1 or (n–1)/2, , (n–1)/2, n–1) for n > 14. In the present paper we study the growth problem for skew and symmetric conference matrices. An algorithm for extending a k × k matrix with elements …
Values Of Minors Of Some Infinite Families Of Matrices Constructed From Supplementary Difference Sets And Their Application To The Growth Problem, C. Koukouvinos, M. Mitrouli, Jennifer Seberry
Values Of Minors Of Some Infinite Families Of Matrices Constructed From Supplementary Difference Sets 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 2v - j minors, j = 0,1, 2 of (1, -1) matrices of order 2v, v odd, where the matrix is constructed using two circulant or type 1 incidence matrices of 2— {v; k1, k2, λ} sds. This allows us to obtain information on the growth problem for families of matrices with moderate growth. Some of our theoretical formulae imply growth close to the order 2v but experimentation has not yet supported this result. An open problem remains to establish whether the (1, -1) CP incidence matrices of certain SBIBDs, can …