Let X be a scheme X and $\mathscr{F}$ be a locally free sheaf of rank $n$ over $X$.
I want to consider a vector bundle over an algebraic variety $X$ , that is ,
the relative spec over $X$ of symmetric algebra of $\mathscr{F}$ ; $V=Spec(Sym \mathscr{F})$.
We write $\rho$ as the natural morphism $V \longrightarrow X$.
Can you define '' transition function of $\rho:V \longrightarrow X$ '' $??$
If it is possible to define that , how can you do it $??$