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Walsh matrix
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<p>In <a href="/facts/Mathematics/pxTouaz4">mathematics</a>, a Walsh matrix is a specific <a href="/facts/Square_matrix/5TP9mNNn">square matrix</a> of dimensions 2<i>n</i>, where <i>n</i> is some particular <a href="/facts/Natural_number/u65og8JE">natural number</a>. The entries of the <a href="/facts/Matrix_(mathematics)/qa8FI4ko">matrix</a> are either +1 or −1 and its rows as well as columns are <a href="/facts/Orthogonal/JVIjYPog">orthogonal</a>. The Walsh matrix was proposed by <a href="/facts/Joseph_L._Walsh/eGYN1jk5">Joseph L. Walsh</a> in 1923. Each row of a Walsh matrix corresponds to a <a href="/facts/Walsh_function/Hqp0MbWv">Walsh function</a>. </p><p>The Walsh matrices are a special case of <i><a href="/facts/Hadamard_matrices/q56o9lgM">Hadamard matrices</a></i> where the rows are rearranged so that the number of sign changes in a row is in increasing order. In short, a Hadamard matrix is defined by the <a href="/facts/Recursion/CxSKxJoW">recursive</a> formula below and is <i>naturally ordered</i>, whereas a Walsh matrix is <i>sequency-ordered</i>. Confusingly, different sources refer to either matrix as the Walsh matrix. </p><p>The Walsh matrix (and Walsh functions) are used in computing the <a href="/facts/Walsh_transform/JFD5uojA">Walsh transform</a> and have applications in the efficient implementation of certain <a href="/facts/Signal_processing/Npaja6zb">signal processing</a> operations. </p>