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翻訳と辞書　辞書検索 [ 開発暫定版 ] スポンサード リンク Walsh matrix ： ウィキペディア英語版 Walsh matrix In mathematics, a Walsh matrix is a specific square matrix with dimensions of some power of 2, entries of +1 or −1, and the property that the dot product of any two distinct rows (or columns) 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 ''natural 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. ==Formula== The Hadamard matrices of dimension 2''k'' for ''k'' ∈ ''N'' are given by the recursive formula The lowest order of Hadamard matrix is 2 :$$ H(2^1) = \begin 1 & 1 \\ 1 & -1 \end, :$$ H(2^2) = \begin 1 & 1 & 1 & 1\\ 1 & -1 & 1 & -1\\ 1 & 1 & -1 & -1\\ 1 & -1 & -1 & 1\\ \end, and in general :$$ H(2^k) = \begin H(2^) & H(2^)\\ H(2^) & -H(2^)\end = H(2)\otimes H(2^), for 2 ≤ ''k'' ∈ ''N'', where $\backslash otimes$ denotes the Kronecker product. 抄文引用元・出典: フリー百科事典『 ウィキペディア（Wikipedia）』 ■ウィキペディアで「Walsh matrix」の詳細全文を読む スポンサード リンク 翻訳と辞書 : 翻訳のためのインターネットリソース Copyright(C) kotoba.ne.jp 1997-2016. All Rights Reserved.