octave: Permutation Matrix Functions

 
 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.