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\end{equation}  As the transpose of the binary matrix is itself. Then, vectors that lead to a symmetric matrix are invarient under the transformation, unless the nature of the vecotrisation has changed such that a column vector is packed into a row vector. Then the transformation is the equivalent of the transpose operation.  Table of 2 vector content from 0 to 3. \begin{equation}  \begin{table}{c|c|c|c|c|}  O & 0 & 1 & 2 & 3 \\  0 & 0,0 & 0,1 & 1,0 & 1,1 \\  1 & 0,2 & 0,3 & 1,2 & 1,3 \\  2 & 2,0 & 2,1 & 3,0 & 3,1 \\  3 & 2,2 & 1,3 & 3,2 & 3,3 \\  \end{table}  \end{equation}