Publication Details

This article was originally published as Kravvaritis, C, Mitrouli, M and Seberry, J, On the growth problem for skew and symmetric conference matrices, Linear Algebra and its Applications, 403, 1 July 2005, 183-206. Copyright Elsevier. Original journal available here.


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 0, ±1 to a skew and symmetric conference matrix of order n is described. By using this algorithm we show the unique W(8, 7) has two pivot structures. We also prove that unique W(10,9) has three pivot patterns.



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