What is meant by the Jordan normal form of an $n \times n$ complex matrix?

Find the Jordan normal forms of the following matrices:

$$\left(\begin{array}{llll} 1 & 1 & 0 & 0 \\ 0 & 1 & 0 & 1 \\ 0 & 0 & 1 & 1 \\ 0 & 0 & 0 & 1 \end{array}\right), \quad\left(\begin{array}{cccc} -1 & -1 & 1 & 0 \\ 0 & -1 & 0 & 1 \\ 0 & 0 & -1 & 1 \\ 0 & 0 & 0 & -1 \end{array}\right), \quad\left(\begin{array}{cccc} 3 & 0 & 0 & 0 \\ 3 & 3 & 0 & 0 \\ 9 & 6 & 3 & 0 \\ 15 & 12 & 9 & 3 \end{array}\right)$$

Suppose $A$ is an invertible $n \times n$ complex matrix. Explain how to derive the characteristic and minimal polynomials of $A^{n}$ from the characteristic and minimal polynomials of $A$. Justify your answer. [Hint: write each polynomial as a product of linear factors.]