Benedict Irwin edited Sketchy Generation.tex  over 9 years ago

Commit id: 03259146fb79e11f6162fadcce41f90414105c77

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\end{equation}  But this means the rank 3 tensor which has depth slices ( the $k^th$ $k^{th}$  matrix $ij$ where $k$ is depth, and $i$ and $j$ are still row and column respectively. We could say the $k^th$ $k^{th}$  shelf in analogy.) \begin{equation} \begin{bmatrix}0 & 0 & 0 \\ 0 & 0 & 1 \\ 0 & -1 & 0\end{bmatrix}_1  \begin{bmatrix}0 & 0 & -1 \\ 0 & 0 & 0 \\ 1 & 0 & 0\end{bmatrix}_2  \begin{bmatrix}0 & 1 & 0 \\ -1 & 0 & 0 \\ 0 & 0 & 0\end{bmatrix}_3  \end{equation}  is equal to the above expansion. This allows us to literally spread out the two by two matrices according to thier entries. Although they all have the form \begin{equation}  \begin{bmatrix} 0 & 1 \\ -1 & 0 \end{bmatrix}  \end{equation}  They undergo individual row and column insertion operations such that \begin{equation}  \begin{bmatrix} 0 & 1 \\ -1 & 0 \end{bmatrix} \to\begin{bmatrix}0 & 0 & 0 \\ 0 & 0 & 1 \\ 0 & -1 & 0\end{bmatrix}_1 \\  \begin{bmatrix} 0 & 1 \\ -1 & 0 \end{bmatrix} \to\begin{bmatrix}0 & 0 & -1 \\ 0 & 0 & 0 \\ 1 & 0 & 0\end{bmatrix}_2 \\  \begin{bmatrix} 0 & 1 \\ -1 & 0 \end{bmatrix} \to\begin{bmatrix}0 & 1 & 0 \\ -1 & 0 & 0 \\ 0 & 0 & 0\end{bmatrix}_3  \end{equation}