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〕
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