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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.