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On the complete pivoting conjecture for Hadamard matrices of small orders
, 2001
"... 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) (n j) minors of Hadamard matrices is presented and its implementation for n = 12 is described. Analytical tables summarizing the pivot patterns attained are giv ..."
Abstract

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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) (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.
An infinite family of Hadamard matrices with fourth last pivot
"... We show that the equivalence class of Sylvester Hadamard matrices give an innite 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 ca ..."
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We show that the equivalence class of Sylvester Hadamard matrices give an innite 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.