A note on subset selection for matrices

In an earlier paper the authors examined the problem of selecting rows of a matrix so that the resulting matrix is as “non-singular” as possible. However, the proof of the key result in that paper is not constructive. In this note we give a constructive proof for that result. In addition, we examine a case where as non-singular as possible means maximizing a determinant and provide a new bound and a constructive proof for this case also.