  <code>S</code>  acts as a reflection;  the faithfulness of this representation (a theorem of Tits) is the main argument to prove that the order of <code>st</code> is exactly <code>m(s,t)</code>. This representation  is defined as follows on a  space <code>V</code> with basis <code>{e‚Çõ}</code> for <code>s‚àà  S</code>. The <em>cartan  matrix</em> associated to  the Coxeter matrix <code>m(s,t)</code> is the matrix <code>C</code> with entries <code>C(s,t)=-2cos(œÄ/m(s,t))</code>; we set <code>C(s