In mathematics

Mathematics

Mathematics is the study of quantity, space, structure, and change. Mathematicians seek out patterns and formulate new conjectures. Mathematicians resolve the truth or falsity of conjectures by mathematical proofs, which are arguments sufficient to convince other mathematicians of their validity...

, in matrix theory, a permutation matrix is a square binary matrix that has exactly one entry 1 in each row and each column and 0s elsewhere. Each such matrix represents a specific permutation

Permutation

In mathematics, the notion of permutation is used with several slightly different meanings, all related to the act of permuting objects or values. Informally, a permutation of a set of objects is an arrangement of those objects into a particular order...

 of m elements and, when used to multiply another matrix, can produce that permutation in the rows or columns of the other matrix. Given a permutation π of m elements,$\backslash pi\; :\; \backslash lbrace\; 1,\; \backslash ldots,\; m\; \backslash rbrace\; \backslash to\; \backslash lbrace\; 1,\; \backslash ldots,\; m\; \backslash rbrace$ given in two-line form by its permutation matrix is the m × m matrix P_π whose entries are all 0 except that in row i, the entry π(i) equals 1.