  We consider the conditions under which the Cayley transform of the Kronecker
product of two Hermitian matrices can be again presented as a Kronecker product
of two matrices and, if so, if it is a product of the Cayley transforms of the
two Hermitian matrices. We also study the related question: given two matrices,
which matrix under the Cayley transform yields the Kronecker product of their
Cayley transforms.
