example of permutation matrix

Consider the matrix


that corresponds to permuting the columns of the identity matrixMathworldPlanetmath under the permutationMathworldPlanetmath (1243) (i.e. (http://planetmath.org/Ie), the first column of the identity matrix is the second column of P, the second column of the identity matrix is the fourth column of P, etc.). Then P is a permutation matrixMathworldPlanetmath.

We will consider what happens when we multiply a 4×4 matrix by P. For example, let A be the matrix




We notice that PA has the same rows as A. Moreover, the rows of A are the rows of PA permuted under (1243): The first row of PA is the second row of A, the second row of PA is the fourth row of A, etc.

Title example of permutation matrix
Canonical name ExampleOfPermutationMatrix
Date of creation 2013-03-22 15:03:14
Last modified on 2013-03-22 15:03:14
Owner Wkbj79 (1863)
Last modified by Wkbj79 (1863)
Numerical id 8
Author Wkbj79 (1863)
Entry type Example
Classification msc 15A36