# Matrix Representation of the Permutation Group

Requires a Wolfram Notebook System

Interact on desktop, mobile and cloud with the free Wolfram Player or other Wolfram Language products.

The set of all permutations of forms a group under the multiplication (composition) of permutations; that is, it meets the requirements of closure, existence of identity and inverses, and associativity. We can set up a bijection between and a set of binary matrices (the permutation matrices) that preserves this structure under the operation of matrix multiplication. The bijection associates the permutation with the matrix , with zeros everywhere except for ones at row, column , for .

Contributed by: Jaime Rangel-Mondragon (August 2012)

Open content licensed under CC BY-NC-SA

## Snapshots

## Details

detailSectionParagraph## Permanent Citation

"Matrix Representation of the Permutation Group"

http://demonstrations.wolfram.com/MatrixRepresentationOfThePermutationGroup/

Wolfram Demonstrations Project

Published: August 2 2012