Publication Details

C. Koukouvinos, M. Mitrouli and Jennifer Seberry, Growth in Gaussian elimination for weighing matrices W(n,n-1), Linear and Multilinear Algebra, 306 (2000), 189-202.


We consider the values for large minors of a skew-Hadamard matrix or conference matrix W of order n and find maximum n x n minor equals to (n-1)n/2, maximum (n-1) x (n-1) minor equals to (n-1)n/2-1, maximum (n-2) x (n-2) minor equals 2(n-1)n/2-2, and maximum (n-3) x (n-3) minor equals to 4(n-1)n/2-3.

This leads us to conjecture that the growth factor for Gaussian elimination of compeletely pivoted skew-Hadamard or conference matrices and indeed any completely pivoted weighing matrix or 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.

We show the unique W(6,5) has a single pivot pattern and the unique W(8,7) has at least two pivot structures. We give two pivot patterns for the unique W(12,11).