|
In mathematics, in matrix theory, a permutation matrix is a square binary matrix that has exactly one entry of 1 in each row and each column and 0s elsewhere. Each such matrix represents a specific permutation of m elements and, when used to multiply another matrix, can produce that permutation in the rows or columns of the other matrix. == Definition == Given a permutation π of ''m'' elements, : given in two-line form by : its permutation matrix acting on m-dimensional column vectors is the ''m × m'' matrix ''P''π whose entries are all 0 except that in row ''i'', the entry π(''i'') equals 1. We may write : where denotes a row vector of length ''m'' with 1 in the ''j''th position and 0 in every other position.〔Brualdi (2006) p.2〕 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「permutation matrix」の詳細全文を読む スポンサード リンク
|