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\section{Gell-Mann matrices}  If we take the Pauli Matrices \begin{equation}  \sigma_1=\begin{bmatrix} 0 & 1 \\ 1 & 0 \end{bmatrix}\\  \sigma_2=\begin{bmatrix} 0 & -i \\ i & 0 \end{bmatrix}\\  \sigma_3=\begin{bmatrix} 1 & 0 \\ 0 & -1 \end{bmatrix}  \end{equation}  and perform the same row column additions as were made to $\epsilon_{ij}$ to get $\epsilon_{ijk}$ we have \begin{equation}  \begin{bmatrix} 0 & 1 \\ 1 & 0 \end{bmatrix} \to  \begin{bmatrix} 0 & 0 & 0 \\ 0 & 0 & 1 \\ 0 & 1 & 0 \end{bmatrix}=\lambda_6\\  \begin{bmatrix} 0 & 1 \\ 1 & 0 \end{bmatrix} \to  \begin{bmatrix} 0 & 0 & 1 \\ 0 & 0 & 0 \\ 1 & 0 & 0 \end{bmatrix}=\lambda_4\\  \begin{bmatrix} 0 & 1 \\ 1 & 0 \end{bmatrix} \to  \begin{bmatrix} 0 & 1 & 0 \\ 1 & 0 & 0 \\ 0 & 0 & 0 \end{bmatrix}=\lambda_1\\  \begin{bmatrix} 0 & i \\ -i & 0 \end{bmatrix} \to  \begin{bmatrix} 0 & 0 & 0 \\ 0 & 0 & -i \\ 0 & i & 0 \end{bmatrix}=\lambda_7\\  \begin{bmatrix} 0 & i \\ -i & 0 \end{bmatrix} \to  \begin{bmatrix} 0 & 0 & -i \\ 0 & 0 & 0 \\ i & 0 & 0 \end{bmatrix}=\lambda_5\\  \begin{bmatrix} 0 & i \\ -i & 0 \end{bmatrix} \to  \begin{bmatrix} 0 & -i & 0 \\ i & 0 & 0 \\ 0 & 0 & 0 \end{bmatrix}=\lambda_2\\  \begin{bmatrix} 1 & 0 \\ 0 & -1 \end{bmatrix} \to  \begin{bmatrix} 1 & 0 & 0 \\ 0 & -1 & 0 \\ 0 & 0 & 0 \end{bmatrix}=\lambda_3\\  \begin{bmatrix} 1 & 0 \\ 0 & -1 \end{bmatrix} \to  \begin{bmatrix} 1 & 0 & 0 \\ 0 & 0 & 0 \\ 0 & 0 & -1 \end{bmatrix}=A\\  \begin{bmatrix} 1 & 0 \\ 0 & -1 \end{bmatrix} \to  \begin{bmatrix} 0 & 0 & 0 \\ 0 & 1 & 0 \\ 0 & 0 & -1 \end{bmatrix}=B\\  \end{equation}  Here $A+B+\lambda_3=\lambda_8$ where $\lambda_i$ are the Gell-Mann matrices.