  The generalized vector is defined on an $n$ dimensional manifold. Interior
product, Lie derivative acting on generalized $p$-forms, $-1\le p\le n$ are
introduced. Generalized commutator of two generalized vectors are defined.
Adding a correction term to Cartan's formula the generalized Lie derivative's
action on a generalized vector field is defined. We explore various identities
of the generalized Lie derivative with respect to generalized vector fields,
and discuss an application.
