deletions | additions       diff --git a/CTW_aims_to_solve.tex b/CTW_aims_to_solve.tex  index 673b65b..5462085 100644  --- a/CTW_aims_to_solve.tex  +++ b/CTW_aims_to_solve.tex 
...
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 $\phi^{T}V^{T}D\phi V=I$} \end{equation}  \begin{equation}  V = \left( \begin{array}{cc} X & 0 \\ 0 & Y \end{array} \right)