Say I have the summations,
$\epsilon\sum_{i=1}^{n}(\alpha^{+(i)} + \alpha^{-(i)})$, where $\epsilon$ is a constant
and $\sum_{i=1}^{n}y^i(\alpha^{+(i)} - \alpha^{-(i)})$
I know that I can change $\sum_{i=1}^{n}(\alpha^{+(i)} + \alpha^{-(i)})$ into \begin{equation} \epsilon \begin{bmatrix} \textbf{1}\\ \textbf{1} \end{bmatrix}^T \begin{bmatrix} \alpha^+\\ \alpha^- \end{bmatrix} \end{equation} where $\textbf{1}$ is a (n x 1) vector.
Similarly, (Correct me if im wrong here) for $\sum_{i=1}^{n}y^i(\alpha^{+(i)} - \alpha^{-(i)})$ I would get,
\begin{equation}
\begin{bmatrix}
\textbf{y}\\ \textbf{-y}
\end{bmatrix}^T
\begin{bmatrix}
\alpha^+\\ \alpha^-
\end{bmatrix}
\end{equation}
So if I performed the operation $\epsilon\sum_{i=1}^{n}(\alpha^{+(i)} + \alpha^{-(i)}) - \sum_{i=1}^{n}y^i(\alpha^{+(i)} - \alpha^{-(i)})$ This would give me,
\begin{equation} \epsilon \begin{bmatrix} \textbf{1}\\ \textbf{1} \end{bmatrix}^T \begin{bmatrix} \alpha^+\\ \alpha^- \end{bmatrix} - \begin{bmatrix} \textbf{y}\\ \textbf{-y} \end{bmatrix}^T \begin{bmatrix} \alpha^+\\ \alpha^- \end{bmatrix} \end{equation} and to further simplify I would get,
\begin{equation} \begin{bmatrix} \epsilon - \textbf{y} \\ \epsilon + \textbf{y} \end{bmatrix}^T \begin{bmatrix} \alpha^+\\ \alpha^- \end{bmatrix} \end{equation}
Can anyone please verify whether what i'm doing is correct. If there is a mistake please explain where, why and how I can fix it. Thank you