Mathematics

A matrix P with the multiplicative property of altering the row or column ordering of a matrix. For example, the LU Decomposition of a matrix, essential to numerical analysis, works best with an LU decomposition of a specially permuted matrix A, i.e.

PA = LU

Permutation matrices can be formed by adjustment of the identity matrix. Left multiplication (e.g. P*A) permutes rows, whereas right multiplication (A*P) permutes columns. For example, the following exercise exchanges rows 2 and 3 of matrix A:

   P        *       A      =      PA

{ 1 0 0        { a b c       { a b c
  0 0 1     *    d e f    =    g h i
  0 1 0 }        g h i }       d e f }

Aside from pedagogical uses, permutation matrices are typically not stored in a dense 2d matrix form, as they can be compactly specified in a 1d vector.