  We study the expectation value of (the product) of the one-particle projector
(s) in the reduced matrix model and matrix quantum mechanics in general. This
quantity is given by the nonabelian Berry phase: we discuss the relevance of
this with regard to the spacetime structure. The case of the USp matrix model
is examined from this respect. Generalizing our previous work, we carry out the
complete computation of this quantity which takes into account both the nature
of the degeneracy of the fermions and the presence of the space time points
belonging to the antisymmetric representation. We find the singularities as
those of the SU(2) Yang monopole connection as well as the pointlike
singularities in 9+1 dimensions coming from its SU(8) generalization. The
former type of singularities, which extend to four of the directions lying in
the antisymmetric representations, may be regarded as seeds of our four
dimensional spacetime structure and is not shared by the IIB matrix model. From
a mathematical viewpoint, these connections can be generalizable to arbitrary
odd space dimensions due to the nontrivial nature of the eigenbundle and the
Clifford module structure.
