Let V be an inner product space over the field $F,T : V \rightarrow V$ is a map on V . If $||T(x) - T(y)|| = || x - y||; \forall x; y \in V$.
Show that there is a $S \in L(V)$ and $v_0 \in V$ such that $T(x) = S(x) + v_0; \forall x; y \in V$
Not sure where to start, would someone please point me in the right direction?