## Permutations as Matrices

Every permutation of a set of integers - or by extension, any set of numbers or objects, can be represented by a matrix. Specifically, a permutation of a set of\[n\]

integers can be represented by a matrix with two rows and n columns.To illustrate consider the permutation

\[(1423)\]

. This permutation sends1 to 4

2 to 3

3 to 1

4 to 2

We can represent this permutation as the matrix

\[ \left( \begin{array}{cccc} 1 & 2 & 3 & 4 \\ 4 & 3 & 1 & 2 \end{array} \right) \]