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Regular Hadamard matrix
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<p>In <a href="/facts/Mathematics/pxTouaz4">mathematics</a> a regular Hadamard matrix is a <a href="/facts/Hadamard_matrix/q56o9lgM">Hadamard matrix</a> whose row and column sums are all equal. While the order of a Hadamard matrix must be 1, 2, or a multiple of 4, regular Hadamard matrices carry the further restriction that the order must be a <a href="/facts/Square_number/jfakASPK">square number</a>. The excess, denoted <i>E</i>(<i>H</i> ), of a Hadamard matrix <i>H</i> of order <i>n</i> is defined to be the sum of the entries of <i>H</i>. The excess satisfies the bound |<i>E</i>(<i>H</i> )| ≤ <i>n</i>3/2. A Hadamard matrix attains this bound <a href="/facts/If_and_only_if/bYSxGJ66">if and only if</a> it is regular. </p>