In mathematics, a Walsh matrix is a specific square matrix of dimensions 2n, where n is some particular natural number. The entries of the matrix are either +1 or −1 and its rows as well as columns are orthogonal, i.e. dot product is zero. The Walsh matrix was proposed by Joseph L. Walsh in 1923. Each row of a Walsh matrix corresponds to a Walsh function. The Walsh matrix (and Walsh functions) are used in computing the Walsh transform and have applications in the efficient implementation of certain signal processing operations.
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| - Matrice di Walsh (it)
- Walsh matrix (en)
- 沃尔什矩阵 (zh)
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| - 沃尔什矩阵（英語：Walsh matrix）是一个维度为的方阵，其中n为自然数。该矩阵由-1和1组成，其所有的行与列都两两正交，即点积为0。这一概念由美国数学家于1923年提出，故而得名。在沃尔什矩阵中，每一行都和一个沃尔什函数相对应。 沃尔什矩阵可视为阿达马矩阵的一个特例，自然有序的阿达马矩阵是由递归公式定义的，序列有序的阿达马矩阵是通过重新排列行来形成的，这样一行中的符号变化数就是递增的。 沃尔什矩阵用于计算沃尔什变换，在信号处理操作中的有实际应用。 (zh)
- In matematica, una matrice di Walsh è una matrice quadrata, avente come numero delle righe e delle colonne una potenza di , con i valori possibili degli elementi della matrice limitati a e , tale che il prodotto scalare fra due righe distinte (o fra due colonne distinte) sia zero. La matrice di Walsh e la sono usate per calcolare la e hanno applicazioni nelle implementazioni efficienti di alcune operazioni che servono al processo dei segnali. (it)
- In mathematics, a Walsh matrix is a specific square matrix of dimensions 2n, where n is some particular natural number. The entries of the matrix are either +1 or −1 and its rows as well as columns are orthogonal, i.e. dot product is zero. The Walsh matrix was proposed by Joseph L. Walsh in 1923. Each row of a Walsh matrix corresponds to a Walsh function. The Walsh matrix (and Walsh functions) are used in computing the Walsh transform and have applications in the efficient implementation of certain signal processing operations. (en)
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| - In mathematics, a Walsh matrix is a specific square matrix of dimensions 2n, where n is some particular natural number. The entries of the matrix are either +1 or −1 and its rows as well as columns are orthogonal, i.e. dot product is zero. The Walsh matrix was proposed by Joseph L. Walsh in 1923. Each row of a Walsh matrix corresponds to a Walsh function. The Walsh matrices are a special case of Hadamard matrices. The naturally ordered Hadamard matrix is defined by the recursive formula below, and the sequency-ordered Hadamard matrix is formed by rearranging the rows so that the number of sign changes in a row is in increasing order. Confusingly, different sources refer to either matrix as the Walsh matrix. The Walsh matrix (and Walsh functions) are used in computing the Walsh transform and have applications in the efficient implementation of certain signal processing operations. (en)
- In matematica, una matrice di Walsh è una matrice quadrata, avente come numero delle righe e delle colonne una potenza di , con i valori possibili degli elementi della matrice limitati a e , tale che il prodotto scalare fra due righe distinte (o fra due colonne distinte) sia zero. La matrice di Walsh può essere ottenuta a partire da una matrice di Hadamard ordinata naturalmente mediante la formula ricorsiva sotto riportata. Nella matrice di Hadamard ordinata sequenzialmente si risistemano le righe in modo che il numero dei cambiamenti di segno sia in ordine crescente. Ogni riga di una matrice di Walsh è associata a una . La matrice di Walsh e la sono usate per calcolare la e hanno applicazioni nelle implementazioni efficienti di alcune operazioni che servono al processo dei segnali. (it)
- 沃尔什矩阵（英語：Walsh matrix）是一个维度为的方阵，其中n为自然数。该矩阵由-1和1组成，其所有的行与列都两两正交，即点积为0。这一概念由美国数学家于1923年提出，故而得名。在沃尔什矩阵中，每一行都和一个沃尔什函数相对应。 沃尔什矩阵可视为阿达马矩阵的一个特例，自然有序的阿达马矩阵是由递归公式定义的，序列有序的阿达马矩阵是通过重新排列行来形成的，这样一行中的符号变化数就是递增的。 沃尔什矩阵用于计算沃尔什变换，在信号处理操作中的有实际应用。 (zh)
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