deletions | additions       diff --git a/Yggm Matrix Properties.tex b/Yggm Matrix Properties.tex  index 923faea..72b1518 100644  --- a/Yggm Matrix Properties.tex  +++ b/Yggm Matrix Properties.tex 
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\section{Properties of $Y_{GGM}$}  %[Work your genius here Ioannis!]  We can now state the following Theorem.\\\\  \textbf{Theorem 3.1.} If every row of the $Y_{bus}$ matrix sums to zero and det$Y_{LL}$=0, then every row of $Y_{GGM}$ sums to zero. If every row of the $Y_{bus}$ matrix sums approximately to zero, or if it sums to zero but det$Y_{LL}$=0, then every row of the matrix $Y_{GGM}$ sums approximately to zero.\\\\  \textbf{Proof.} The matrix $Y_{GGM}$can be written as 
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\[  Z_{LL}=\left\{\begin{array}{c}Y_{LL}^{-1},\quad det(Y_{LL})\neq 0\\Y_{LL}^\dagger,\quad det(Y_{LL})=0\end{array}\right\}.  \]  Let $Y_{GG}=[a_{ij}]_{i=1,2,...,m}^{j=1,2,...,m}$, $Y_{GL}=[b_{ij}]_{i=1,2,...,m}^{j=1,2,...,n}$, $F_{LG}=[c_{ij}]_{i=1,2,...,n}^{j=1,2,...,m}$ , $Y_{GL}F_{LG}=[d_{ij}]_{i=1,2,...,m}^{j=1,2,...,m}$ and $Y_{GGM}=[g_{ij}]_{i=1,2,...,m}^{j=1,2,...,m}$. By substituting the previous expressions into \eqref{eq1}, for every row $i=1,2,...,m$ we have \begin{equation}\label{eq2}  \sum_{j=1}^mg_{ij}=\sum_{j=1}^ma_{ij}+\sum_{j=1}^md_{ij}.  \end{equation}