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These matrices are constructed from the rows of the original matrix as such, if R_i is the ith row of the original matrix, and P_n is an operator which cycles that row forward n times we have \begin{equation}  A^{TL}=\begin{bmatrix} R_2^TP_2 & R_1^TP_1 & R_1^TP_2 \end{bmatrix} \\ =A^{r(211)}_{p(212)}\\  A^{TR}=\begin{bmatrix} R_2^TP_1 & R_1^TP_2 & R_1^TP_1 \end{bmatrix} \\ =A^{r(211)}_{p(121)}\\  A^{BL}=\begin{bmatrix} R_3^TP_2 & R_3^TP_1 & R_2^TP_2 \end{bmatrix} \\ =A^{r(332)}_{p(212)}\\  A^{BR}=\begin{bmatrix} R_3^TP_1 & R_3^TP_2 & R_2^TP_1 \end{bmatrix} =A^{r(332)}_{p(121)}  \end{equation}