title: solving Ax =b for a non-square matrix A using python
body: <p>I'm focusing on the special case where <code>A</code> is a n x d matrix (where k &lt; d) representing an orthogonal basis for a subspace of R^d and b is known to be inside the subspace.
  I thought of using the tools provided with <code>numpy</code>, however they only work with square matrices. I had the approach of filling in the matrix with some linearly independent vectors to "square" it and then solve, but I could not figure out how to choose those vectors so that they will be linearly independent of the basis vectors, plus I think it's not the only approach and I'm missing something that can make this easier.
  is there indeed a simpler approach than the one I mentioned? if not, how indeed do I choose those vectors that would complete <code>A</code>into a square matrix?</p>