✦ LIBER ✦

On the growth problem for skew and symmetric conference matrices

✍ Scribed by C. Kravvaritis; M. Mitrouli; Jennifer Seberry

Publisher: Elsevier Science
Year: 2005
Tongue: English
Weight: 271 KB
Volume: 403
Category: Article
ISSN: 0024-3795
DOI: 10.1016/j.laa.2005.02.001

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✦ Synopsis

Koukouvinos et al.

[C. Koukouvinos, M. Mitrouli, J. Seberry, Growth in Gaussian elimination for weighing matrices, W (n, n -1), Linear Algebra 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 that the unique W (8, 7) has two pivot structures. We also prove that the unique W (10, 9) has three pivot patterns.

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