deletions | additions       diff --git a/CTW_aims_to_solve.tex b/CTW_aims_to_solve.tex  index d0994ba..24456c8 100644  --- a/CTW_aims_to_solve.tex  +++ b/CTW_aims_to_solve.tex 
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We can also restrict the mapping to be linear by instead solving the optimization problem:  \begin{equation}  \label{eqn:linearmaeqn} \underset{\phi}{\arg\min} \left(tr\left(\phi^{T}V^{T}L\phi V\right)\right) \mbox{subject to ...}  \end{equation}  \begin{equation}  V = \left( \begin{array}{cc} X & 0 \\ 0 & Y \end{array} \right)