sidebar interaction. Press tab to begin. Note that \left\{ \begin{bmatrix} 1 \\ 0 \end{bmatrix} , \begin{bmatrix} 0 \\ 1 \end{bmatrix} ight \} is only one possible basis of the eigenspace for this particular example. Any other basis of \mathbb{R}^2 is a basis of the eigenspace. For instance, \left\{ \begin{bmatrix} 2 \\ 3 \end{bmatrix} , \begin{bmatrix} 1 \\ 1 \end{bmatrix} ight \}, \left\{ \begin{bmatrix} -1 \\ 7 \end{bmatrix} , \begin{bmatrix} 5 \\ 18 \end{bmatrix} ight \}, ... are basis of the eigenspace. In general, any set of two linearly independent vectors is a basis of the eigenspace