Let A=[1234012300120001]A = \begin{bmatrix} 1 & 2 & 3 & 4 \\ 0 & 1 & 2 & 3 \\ 0 & 0 & 1 & 2 \\ 0 & 0 & 0 & 1 \end{bmatrix}A=1000210032104321. What is the dimension spanned by the eigenvectors of AAA?
