Jordan canonical form (from the January 2002 qualifying exam):
Let A be the matrix
[-1 -9 0 0]
[ 1 5 0 0]
[ 2 7 2 0]
[ 4 13 0 2]
- (a) Show that the characteristic polynomial is
(t - 2)^{4}.
- (b) Find the Jordan canonical form J of A. Justify your answer.
- (c) We know J = P^{-1}AP. Find either P or P^{-1}
(your choice), but be sure to indicate which it is you've found.