  In this paper, we give the matrix version of Horn's hypergeometric function
and its confluent cases. We also discuss the regions of convergence, the system
of matrix differential equations of bilateral type, differential formulae and
infinite summation formulae satisfied by these hypergeometric matrix functions.
We also give the certain integral representation of these hypergeometric matrix
functions. The study of these 23 matrix functions leads to completing the
matrix generalization of Horn's list of 34 hypergeometric series.
