deletions | additions       diff --git a/Sketchy Generation.tex b/Sketchy Generation.tex  index 0c49675..6e18196 100644  --- a/Sketchy Generation.tex  +++ b/Sketchy Generation.tex 
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\end{equation}  holds. A vector of matrices. For our $S$ operation we can swap a row in the initial matrix, however this just equates to minus the result. \begin{equation}  \hat{S}\textbf{r}_1 = \begin{vmatrix} \textbf{i} & \textbf{j} & \textbf{k} \\ \textbf{i} & \textbf{j} & \textbf{k} \\ x_1 & y_1 & z_1 \end{vmatrix} = \begin{bmatrix} 0 & z_1 & -y_1 \\ -z_1 & 0 & x_1 \\ y_1 & -x_1 & 0 \end{bmatrix} \\ \\  \hat{S}'\textbf{r}_1 = \begin{vmatrix} \textbf{i} & \textbf{j} & \textbf{k} \\ x_1 & y_1 & z_1 \\ \textbf{i} & \textbf{j} & \textbf{k} \end{vmatrix} = \begin{bmatrix} 0 & -z_1 & y_1 \\ z_1 & 0 & -x_1 \\ -y_1 & x_1 & 0 \end{bmatrix} \\ \\  \end{equation}