(octave.info)Creating Permutation Matrices

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21.1.2 Creating Permutation Matrices
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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”.