  A finite or infinite matrix $A$ is image partition regular provided that
whenever $\mathbb{N}$ is finitely colored, there must be some
$\overset{\rightarrow}{x}$ with entries from $\mathbb{N}$ such that all entries
of $A \overset{\rightarrow}{x}$ are in the same color class. Comparing to the
finite case, infinite image partition regular matrices seem more harder to
analyze. The concept of centrally image partition regular matrices were
introduced to extend the results of finite image partition regular matrices to
infinite one. In this paper, we shall introduce the notion of C-image partition
regular matrices, an interesting subclass of centrally image partition regular
matrices. Also we shall see that many of known centrally image partition
regular matrices are C-image partition regular.
