  We propose a new matrix model describing multi-baryon systems. We derive the
action from open string theory on the wrapped baryon vertex D-branes embedded
in the D4-D8 model of large N holographic QCD. The positions of k baryons are
unified into k x k matrices, with spin/isospin of the baryons encoded in a set
of k-vectors. Holographic baryons are known to be very small in the large 't
Hooft coupling limit, and our model offers a better systematic approach to
dynamics of such baryons at short distances. We compute energetics and spectra
(k=1), and also short-distance nuclear force (k=2). In particular, we obtain a
new size of the holographic baryon and find a precise form of the repulsive
core of nucleons. This matrix model complements the instanton soliton picture
of holographic baryons, whose small size turned out to be well below the
natural length scale of the approximation involved there. Our results show
that, nevertheless, the basic properties of holographic baryons obtained there
are robust under stringy corrections within a few percents.
