Matrix Representation of the Permutation Group

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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
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"Matrix Representation of the Permutation Group"
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Published: August 2 2012