7. For $n \geqslant 0$ we define the vector $U _ { n } \in \mathbb { C } ^ { d }$ by $U _ { n } = \left( u _ { n } , \ldots , u _ { n + d - 1 } \right)$ (recall that $U _ { n }$ is identified with a column vector). Show that the sequence $( U _ { n } )$ satisfies a recurrence relation of the form $U _ { n + 1 } = A U _ { n } + B$, with $A \in \mathrm { M } _ { d } ( \mathbb { C } )$ and $B \in \mathbb { C } ^ { d }$ are elements that we will specify.