Editing Generalized permutation matrix (section)

== Properties ==
* If a nonsingular matrix and its inverse are both [[nonnegative matrices]] (i.e. matrices with nonnegative entries), then the matrix is a generalized permutation matrix.
* The determinant of a generalized permutation matrix is given by <math display="block">\det(G)=\det(P)\cdot \det(D)=\operatorname{sgn}(\pi)\cdot d_{11}\cdot \ldots \cdot d_{nn},</math> where <math>\operatorname{sgn}(\pi)</math> is the [[sign of a permutation|sign]] of the [[permutation]] <math>\pi</math> associated with <math>P</math>  and <math>d_{11},\ldots ,d_{nn}</math> are the diagonal elements of <math>D</math>.