Table 2 Matrices for conversion of isotopomer and mass fraction vectors
From: Modeling framework for isotopic labeling of heteronuclear moieties
\(\overline{\mathbf{IM }}_{n,m}\) | \(n=0\) | \(n=1\) | \(n=2\) |
|---|---|---|---|
\(m=0\) | \(\begin{bmatrix} 1 \end{bmatrix}\) | \(\begin{bmatrix} 1 \end{bmatrix}\) | \(\begin{bmatrix} 1 \end{bmatrix}\) |
\(m=1\) | \(\begin{bmatrix} 1 \end{bmatrix}\) | \(\begin{bmatrix} 1&0\\ 0&1 \end{bmatrix}\) | \(\begin{bmatrix} 1&0&0&0\\ 0&1&1&0\\ 0&0&0&1 \end{bmatrix}\) |
\(m=2\) | \(\begin{bmatrix} 1 \end{bmatrix}\) | \(\begin{bmatrix} 1&0&0\\ 0&1&0\\ 0&0&1 \end{bmatrix}\) | \(\begin{bmatrix} 1&0&0&0&0&0&0&0&0\\ 0&1&0&1&0&0&0&0&0\\ 0&0&1&0&1&0&1&0&0\\ 0&0&0&0&0&1&0&1&0\\ 0&0&0&0&0&0&0&0&1 \end{bmatrix}\) |