Permutation matrices

How we deal with permutation matrices?

In Magma, vectors are row vectors and permutation matrices act on the right. For a permutation $\sigma$, the corresponding permutation matrix constructed with PermutationMatrix permutes the coordinates according to $\sigma$. Here is an example corresponding to the permutation $\sigma=(1234)\in\mathbb{S}_5$:

> m := PermutationMatrix(Integers(), [2,3,4,1,5]);
> v := Vector(Integers(), [0,0,0,0,1]);
> v*m;
(0 0 0 0 1)
> w := Vector(Integers(), [1,0,0,0,0]);
> w*m;
(0 1 0 0 0)

Here is another example:

> s := Sym(3)!(1,2);
> m := PermutationMatrix(Integers(), [ x^s : x in [1,2,3] ]);
> m;
[0 1 0]
[1 0 0]
[0 0 1]
> Vector(Integers(), [0,1,0])*m;
(1 0 0)
> Vector(Integers(), [0,0,1])*m;
(0 0 1)