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\section{Matrix Generators}  Certain matrices are more fundamental under certain interpretations, one could use the determinant as a matrix generator for example \begin{equation}  \begin{vmatrix}  \textbf{i} & \textbf{j} \\ \textbf{-i} & \textbf{j}  \end{vmatrix}  =  \begin{bmatrix}  0 & 1 \\ 1 & 0  \end{bmatrix}  =\sigma_x  \\  \begin{vmatrix}  \textbf{i} & \textbf{j} \\ \textbf{i} & \textbf{j}  \end{vmatrix}  =  \begin{bmatrix}  0 & 1 \\ -1 & 0  \end{bmatrix}  =i\sigma_y  \\  \begin{vmatrix}  \textbf{i} & \textbf{j} \\ \textbf{j} & \textbf{i}  \end{vmatrix}  =  \begin{bmatrix}  1 & 0 \\ 0 & -1  \end{bmatrix}  =\sigma_z  \end{equation}