title: Rank of matrices with just a different column
body: <p>I am currently writing a code in Matlab where I have to compute a ton of rank of matrices, a ton being from millions to billions or hopefully more. The most, the better.</p>
  
  <p>These matrices usually differ, at each step, for just one column, of which I know the position. I was wondering if there was any "fast" algorithm, faster than Matlab one which uses svd, to compute the rank of such a family of matrices.</p>
  
  <p>Additional info: Matrices are not very big, size being at most 100x100 and they are sparse.</p>
  
  <p>Thanks in advance to anyone who could give some help.</p>