(octave.info)Permutation Matrix Functions

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21.3.2 Permutation Matrix Functions
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“inv” and “pinv” will invert a permutation matrix, preserving its
specialness.  “det” can be applied to a permutation matrix, efficiently
calculating the sign of the permutation (which is equal to the
determinant).

   A permutation matrix can also be returned from the built-in functions
“lu” and “qr”, if a pivoted factorization is requested.

   The “sparse” function will convert a permutation matrix efficiently
to a sparse matrix.  The “find” function will also work efficiently with
a permutation matrix, making it possible to conveniently obtain the
permutation indices.