A \sim D_{1}=\left ( \begin{array}{ccc} 1 & 0 & \dots \ 0 \\0 & 0 & \dots \ 0 \\ \vdots & \vdots & \ddots \ \ \vdots \\ 0 & 0 & \dots \ 0 \end{array} \right)=\left ( \begin{array}{ccc} 1 \\ 0 \\ 0 \\ \vdots \\ 0 \end{array} \right) \left ( \begin{array}{ccc} 1 & 0 & \dots \ 0 \end{array} \right )