  As a substantial generalization of the technique for constructing canonical
and the related nonlinear and q-deformed coherent states, we present here a
method for constructing vector coherent states in the same spirit. These vector
coherent states may have a finite or an infinite number of components. As
examples we first apply the technique to construct vector coherent states using
the Plancherel isometry for groups and vector coherent states associated to
Clifford algebras, in particular quaternions. As physical examples, we discuss
vector coherent states for a quantum optical model and finally apply the
general technique to build vector coherent states over certain matrix domains.
