The matrix $A=\begin{bmatrix} 0 & 1 & 0 & 0 \\ 0 & 0 & 0 & 0 \\ 0 & 0 & 0 & 1 \\ 0 & 0 & 0 & 0 \end{bmatrix}$ has eigenvalue $\lambda=0$ of multiplicity $4$. Solving $(A-\lambda I)v=0$ for $\lambda=0$ only get two eigenvectors:
$v_1=\begin{bmatrix} 1 \\ 0 \\ 0 \\ 0 \end{bmatrix}$ and $v_2=\begin{bmatrix} 0 \\ 0 \\ 1 \\ 0 \end{bmatrix}$. So can I say the eigenspace corresponding to $\lambda=0$ is equal to $Span(v_1,v_2)$? Or do I need four vectors to form the eigenspace, and if I do need 4 then how do I find the other two to form the eigenspace?