High Quality Content by WIKIPEDIA articles! Hadamard's maximal determinant problem, named after Jacques Hadamard, asks for the largest determinant of a matrix with elements equal to 1 or ?1. The analogous question for matrices with elements equal to 0 or 1 is equivalent since the maximal determinant of a {1,?1} matrix of size n is 2n?1 times the maximal determinant of a {0,1} matrix of size n?1. The problem was posed by Hadamard in the 1893 paper in which he presented his famous determinant bound and remains unsolved for matrices of general size. Hadamard's bound implies that {1, ?1}-matrices of size n have determinant at most nn/2. Hadamard observed that a construction of Sylvester produces examples of matrices that attain the bound when n is a power of 2, and produced examples of his own of sizes 12 and 20. He also showed that the bound is only attainable when n is equal to 1, 2, or a multiple of 4. Additional examples were later constructed by Scarpis and Paley and subsequently by...

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