For creating permutation matrices, Octave does not introduce a new function,
but rather overrides an existing syntax: permutation matrices can be
conveniently created by indexing an identity matrix by permutation vectors.
That is, if `q` is a permutation vector of length `n`, the expression

P = eye (n) (:, q);

will create a permutation matrix - a special matrix object.

eye (n) (q, :)

will also work (and create a row permutation matrix), as well as

eye (n) (q1, q2).

For example:

eye (4) ([1,3,2,4],:) ⇒ Permutation Matrix 1 0 0 0 0 0 1 0 0 1 0 0 0 0 0 1 eye (4) (:,[1,3,2,4]) ⇒ Permutation Matrix 1 0 0 0 0 0 1 0 0 1 0 0 0 0 0 1

Mathematically, an identity matrix is both diagonal and permutation matrix.
In Octave, `eye (n)`

returns a diagonal matrix, because a matrix
can only have one class. You can convert this diagonal matrix to a permutation
matrix by indexing it by an identity permutation, as shown below.
This is a special property of the identity matrix; indexing other diagonal
matrices generally produces a full matrix.

eye (3) ⇒ Diagonal Matrix 1 0 0 0 1 0 0 0 1 eye(3)(1:3,:) ⇒ Permutation Matrix 1 0 0 0 1 0 0 0 1

Some other built-in functions can also return permutation matrices. Examples
include
*inv* or *lu*.