在线性空间 $\mathrm{R}^{2 \times 2}$ 中, $\alpha_1=\left(\begin{array}{ll}1 & 0 \\ 0 & 0\end{array}\right), \quad \alpha_2=\left(\begin{array}{ll}1 & 1 \\ 0 & 0\end{array}\right), \alpha_3=\left(\begin{array}{ll}1 & 1 \\ 1 & 0\end{array}\right), \quad \alpha_4=\left(\begin{array}{ll}1 & 1 \\ 1 & 1\end{array}\right)$ 是 一个基, 则向量 $\alpha=\left(\begin{array}{ll}1 & 2 \\ 3 & 4\end{array}\right)$ 在该基下的坐标为