On ordering properties of generalized inverses of nonnegative definite matrices (Q2365679)

A partial ordering is defined on the set of nonnegative definite matrices of the same size by \(A\geq B\) if \(A-B\) is nonnegative definite. Suppose that \(A\geq B\). This paper characterizes when nonnegative definite generalized inverses \(A^ +\) and \(B^ +\) satisfy \(B^ +\geq A^ +\). Other questions about this ordering and generalized inverses are also considered.