title: Construct a full rank matrix by adding vectors from the standard basis
body: <p>I have a nxn singular matrix. I want to add k rows (which must be from the standard basis e1, e2, ..., en) to this matrix such that the new (n+k)xn matrix is full column rank. The number of added rows k must be minimum and they can be added in any order (not just e1, e2 ,..., it can be e4, e10, e1, ...) as long as k is minimum.</p>
  
  <p>Does anybody know a simple way to do this? Any help is appreciated.</p>