On the linear hull of a weighted automaton

Previous work reduces the problem of deciding whether a weighted finite automaton (WFA) over a field is equivalent to a deterministic, respectively, unambiguous, WFA to the computation of the linear hull. The linear hull is the topological closure of the reachability set in a linear version of the Zariski topology. We discuss this invariant and its computability, staying in the realm of linear algebra (e.g., not first computing the finer Zariski topology), as far as possible. This talk is on joint work with J. Bell.