  As a sequel to Kawakami-Nakamura-Sakai (arXiv:1209.3836), this series of
papers constructs the complete degeneration scheme of four-dimensional
Painlev\'e-type equations which includes the Painlev\'e-type equations
associated with linear systems of ramified type. In the present paper, we
consider the degeneration of Painlev\'e-type equations which we call the matrix
Painlev\'e systems.
