  A class of vector coherent states is derived with multiple of matrices as
vectors in a Hilbert space, where the Hilbert space is taken to be the tensor
product of several other Hilbert spaces. As examples vector coherent states
with multiple of quaternions and octonions are given. The resulting generalized
oscillator algebra is briefly discussed. Further, vector coherent states for a
tensored Hamiltonian system are obtained by the same method. As particular
cases, coherent states are obtained for tensored Jaynes-Cummings type
Hamiltonians and for a two-level two-mode generalization of the Jaynes-Cummings
model.
