  We examine some properties of the non-normalized (or canonical) density
matrix in the coherent states representation, by two equivalent ways. On the
one hand by its definition, and on the other hand as a solution to Bloch's
canonical equation. It is concluded that, since in many cases Bloch's
differential equation is difficult to solve, in applications it is preferable
to use the expression obtained directly from the definition of the canonical
density matrix in the coherent states representation. This conclusion is
verified by examining several cases of quantum systems with linear or quadratic
energy spectrum.
