Document Type
Journal Article
RIS ID
19433
Abstract
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.
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.