For an operator \(T \in \mathcal{L}(V)\), \(T^{n}\) would make sense. Instead of writing \(TTT\dots\), then, we just write \(T^{n}\).

## constituents

- operator \(T \in \mathcal{L}(V)\)

## requirements

- \(T^{m} = T \dots T\)

## additional information

### \(T^{0}\)

\begin{equation} T^{0} := I \in \mathcal{L}(V) \end{equation}

### \(T^{-1}\)

\begin{equation} T^{-m} = (T^{-1})^{m} \end{equation}

**if** \(T\) is invertable

### usual rules of squaring

\begin{equation} \begin{cases} T^{m}T^{n} = T^{m+n} \\ (T^{m})^{n} = T^{mn} \end{cases} \end{equation}

This can be shown by counting the number of times \(T\) is repeated by writing each \(T^{m}\) out.