Nowadays, I'm studying for exponential map of Lie group.
my question is, To make the form of exp$\begin{pmatrix}x_{11}&x_{12}&\cdots \\x_{21}&\ddots \\ \vdots\end{pmatrix}$,
I have to multiply same matrixes. so I wonder more basically, when the matrix $A$ which has all component can be arbitrary number, although we make $A^N$,whether $A^N$ has also all component which can be arbitrary number or not.
additionally, My major is physics, by the way, I almost don't know about mathematic symbols. If you know the process of proof, please show me the proof without mathematic symbols possible.