The generalized inverse of integral matrices

AbstractThe generalized inverse or Moore-Penrose-inverse of a real m × n matrix A is known to be the unique n × m matrix A∗ satisfying the conditions (GI.1) and (GI.2) below. For a rational matrix A the generalized inverse turns out to be rational, too. Hence given an integral matrix A the description of the denominator of A∗ is of interest and yields some new integral invariants of A