title: Finding m-linearly independent columns of a matrix on MATLAB
body: <p>Let us have a linear system Ax&lt;= b. To find a vertex of this polyhedral set we need to choose m linearly independent columns of A and solve the system with the corresponding variables. How can I generate <strong>all</strong> the m-linearly-independent columns using MATLAB? I will then find all the vertices of the polyhedron I have.</p>
  
  <p>What I can think about is: generate all the (n, m) combination of subsets. Check one by one ranks. Whenever the ranks are =m, take these solutions since they have full m-rank. Is there a more efficient method?</p>