deletions | additions       diff --git a/Sketchy Generation.tex b/Sketchy Generation.tex  index b8a007e..d40a895 100644  --- a/Sketchy Generation.tex  +++ b/Sketchy Generation.tex 
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The difference of these two then appears to be the introduction of rows of $i,j,k$ in the determinant and the removal of vector inputs. Above are a binary and ternary operation, experimenting with this concept in the same notation we can generate a unary operation and a 0-ary operation, i.e just an object. We have \begin{equation}  \textbf{r}_1 \to \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} \\ \\ \begin{vmatrix} \textbf{i} & \textbf{j} & \textbf{k} \\ \textbf{i} & \textbf{j} & \textbf{k} \\ \textbf{i} & \textbf{j} & \textbf{k} \end{vmatrix}= \epsilon_{ijk} 
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The first operation takes a vector and generates a skew symmetric matrix. The third operation defines the Levi-Civita symbol, a rank $3$ tensor which is essential to vector calculus. A use of the first operation would be to define the electromagnetic tensor which looks like \begin{equation}  F_{\mu\nu}=\begin{bmatrix} 0 & E_x/c & E_y/c & E_z/c \\ -E_x/c & 0 & B_z & -B_y \\ -E_y/c & -B_z & 0 & B_x \\ -E_z/c & B_y & -B_x & 0 \end{bmatrix}  \end{equation} Here we can see the lower right 3x3 matrix would just be $\hat{S}\textbf{B}$...