Physical Sciences and Mathematics Commons^™

Growth In Gaussian Elimination For Weighing Matrices, W (N, N — 1), C. Koukouvinos, M. Mitrouli, Jennifer Seberry

Faculty of Informatics - Papers (Archive)

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 to 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 completely pivoted skew-Hadamard or conference matrices and indeed any completely pivoted weighing matrix of order …