Find the eigenvalues and a basis for the each of the eigenspaces of the following matrices. Which are complete?
(a) $\left(\begin{array}{rr}4 & -4 \\ 1 & 0\end{array}\right)$
(b) $\left(\begin{array}{ll}6 & -8 \\ 4 & -6\end{array}\right)$,
(c) $\left(\begin{array}{ll}3 & -2 \\ 4 & -1\end{array}\right)$,
(d) $\left(\begin{array}{rr}\mathrm{i} & -1 \\ 1 & \mathrm{i}\end{array}\right)$,
(e) $\left(\begin{array}{rrr}4 & -1 & -1 \\ 0 & 3 & 0 \\ 1 & -1 & 2\end{array}\right)$,
(f) $\left(\begin{array}{rrr}-6 & 0 & -8 \\ -4 & 2 & -4 \\ 4 & 0 & 6\end{array}\right)$,
(g) $\left(\begin{array}{rrr}-2 & 1 & -1 \\ 5 & -3 & 6 \\ 5 & -1 & 4\end{array}\right)$,
(h) $\left(\begin{array}{rrrr}1 & 0 & 0 & 0 \\ 0 & 1 & 0 & 0 \\ -1 & 1 & -1 & 0 \\ 1 & 0 & -1 & 0\end{array}\right)$,
(i) $\left(\begin{array}{rrrr}-1 & 0 & 1 & 2 \\ 0 & 1 & 0 & 1 \\ -1 & -4 & 1 & -2 \\ 0 & 1 & 0 & 1\end{array}\right)$.