Table 2.

Matrices for conversion of isotopomer and mass fraction vectors

${\overline{\mathbf{IM}}}_{n,m}$	$n=0$	$n=1$	$n=2$
$m=0$	$\left[\begin{array}{c}1\end{array}\right]$	$\left[\begin{array}{c}1\end{array}\right]$	$\left[\begin{array}{c}1\end{array}\right]$
$m=1$	$\left[\begin{array}{c}1\end{array}\right]$	$\left[\begin{array}{cc}1& 0\\ 0& 1\end{array}\right]$	$\left[\begin{array}{cccc}1& 0& 0& 0\\ 0& 1& 1& 0\\ 0& 0& 0& 1\end{array}\right]$
$m=2$	$\left[\begin{array}{c}1\end{array}\right]$	$\left[\begin{array}{ccc}1& 0& 0\\ 0& 1& 0\\ 0& 0& 1\end{array}\right]$	$\left[\begin{array}{ccccccccc}1& 0& 0& 0& 0& 0& 0& 0& 0\\ 0& 1& 0& 1& 0& 0& 0& 0& 0\\ 0& 0& 1& 0& 1& 0& 1& 0& 0\\ 0& 0& 0& 0& 0& 1& 0& 1& 0\\ 0& 0& 0& 0& 0& 0& 0& 0& 1\end{array}\right]$