Dear Linear Algebra Experts,
I am preparing for my exams and currently stuck with following problem. The following question may be trivial for you, but I don't know how to solve it. I would really appreciate your help.
The linear transformation $d/dt : x(t) → x^\prime(t)$ acting on the vector space of all polynomials with degree at most 3 has the basis representation $$ \begin{bmatrix} 0 &1 &0 &0 \\ 0 &0 &2 &0 \\ 0 &0 &0 &3 \\ 0 &0 &0 &0 \end{bmatrix} $$ in the basis $T = \left\{1, t, t^2, t^3\right\}$. What is the Jordan canonical form of this matrix?