The generalized inverse of integral matrices (Q1066976)

Let A and b be a real integral matrix and a vector. Characterizations are given that the Moore-Penrose inverse \(A^+\) of A be integral and also that there exists an integral solution of the diophantine equation \(Ax=b\). Sample result: The latter is equivalent to \(AA^+b=b\) and \(g^ tA^+b\in {\mathbb{Z}}\) for all \(g\in {\mathbb{Z}}^ n\) such that \(A^+Ag=g\).