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Full-Text Articles in Physical Sciences and Mathematics
On The Growth Problem For Skew And Symmetric Conference Matrices, C. Kravvaritis, M. Mitrouli, Jennifer Seberry
On The Growth Problem For Skew And Symmetric Conference Matrices, C. Kravvaritis, M. Mitrouli, Jennifer Seberry
Faculty of Informatics - Papers (Archive)
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 …
An Infinite Family Of Hadamard Matrices With Fourth Last Pivot N/2, C. Koukouvinos, M. Mitrouli, Jennifer Seberry
An Infinite Family Of Hadamard Matrices With Fourth Last Pivot N/2, C. Koukouvinos, M. Mitrouli, Jennifer Seberry
Faculty of Informatics - Papers (Archive)
We show that the equivalence class of Sylvester Hadamard matrices give an infinite family of Hadamard matrices in which the fourth last pivot is n/2 . Analytical examples of Hadamard matrices of order n having as fourth last pivot n/2 are given for n = 16 and 32. In each case this distinguished case with the fourth pivot n/2 arose in the equivalence class containing the Sylvester Hadamard matrix.
On The Complete Pivoting Conjecture For Hadamard Matrices Of Small Orders, C. Koukouvinos, M. Mitrouli, Jennifer Seberry
On The Complete Pivoting Conjecture For Hadamard Matrices Of Small Orders, C. Koukouvinos, M. Mitrouli, Jennifer Seberry
Faculty of Informatics - Papers (Archive)
In this paper we study explicitly the pivot structure of Hadamard matrices of small orders 16, 20 and 32. An algorithm computing the (n — j) x (n — j) minors of Hadamard matrices is presented and its implementation for n = 12 is described. Analytical tables summarizing the pivot patterns attained are given.
Growth In Gaussian Elimination For Weighing Matrices, W (N, N — 1), C. Koukouvinos, M. Mitrouli, Jennifer Seberry
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 …