
Jordan form
Would you help me with this:
Let A is in C^4. A =
( 0 0 0 1
1 0 0 2
0 1 0 2
0 0 1 2)
(i)Determine the minimal characteristic polynomials of A.
(ii) Determine the Jordan form of A.
(iii) Construct a basis B of C^4 such that [T_A]_B is in Jordan form , where T_A is the linear map T_A: > C4 : X > AX.
Thank you!

Start by computing the eigenvalues from the $\displaystyle c_A(x)$ and then the eigenvectors.. put the eigenvectors in diagonalizable form $\displaystyle P$ such that $\displaystyle P^1AP= D $ which is your jordan block form. The new basis B will just be the basis of eigenspaces.