title: Generate a vector that is orthogonal to a set of other vectors in any dimension
body: <p>Assume I have a set of vectors $ a_1, ..., a_d $ that are orthonormal to each other. Now, I want to find another vector $ a_{d+1} $ that is orthogonal to all the other vectors.</p>
  
  <ol>
  <li><p>Is there an efficient algorithm to achieve this? I can only think of adding a random vector to the end, and then applying gram-schmidt.</p></li>
  <li><p>Is there a python library which already achieves this? </p></li>
  </ol>