  In this work we address the classical problem of classifying tuples of linear
operators and linear functions on a finite dimensional vector space up to base
change. Having adopted for the situation considered a construction of framed
moduli spaces of quivers, we develop an explicit classification of tuples
belonging to a Zariski open subset. For such tuples we provide a finite family
of normal forms and a procedure allowing to determine whether two tuples are
equivalent.
