  We revisit the Vectorial Lambda Calculus, a typed version of Lineal.
Vectorial (as well as Lineal) has been originally designed for quantum
computing, as an extension to System F where linear combinations of lambda
terms are also terms and linear combinations of types are also types. In its
first presentation, Vectorial only provides a weakened version of the Subject
Reduction property. We prove that our revised Vectorial Lambda Calculus
supports the standard version of said property, answering a long standing
issue. In addition we also introduce the concept of weight of types and terms,
and prove a relation between the weight of terms and of its types.
