  The general transformation of the product of coherent states
$\prod_{i=1}^N|\alpha_i>$ to the output state $\prod_{i=1}^M|\beta_i>$ ($N=M$
or $N\neq M$), which is realizable with linear optical circuit, is
characterized with a linear map from the vector
$(\alpha^{\ast}_1,...,\alpha^{\ast}_N)$ to
$(\beta^{\ast}_1,...,\beta^{\ast}_M)$. A correspondence between the
transformations of a product of coherent states and those of a single photon
state is established with such linear maps. It is convenient to apply this
linear transformation method to design any linear optical scheme working with
coherent states. The examples include message encoding and quantum database
searching. The limitation of manipulating entangled coherent states with linear
optics is also discussed.
