  In gauge/gravity duality, matrix degrees of freedom on the gauge theory side
play important roles for the emergent geometry. In this paper, we discuss how
the entanglement on the gravity side can be described as the entanglement
between matrix degrees of freedom. Our approach, which we call 'matrix
entanglement', is different from 'target-space entanglement' proposed and
discussed recently by several groups. We consider several classes of quantum
states to which our approach can play important roles. When applied to fuzzy
sphere, matrix entanglement can be used to define the usual spatial
entanglement in two-brane or five-brane world-volume theory nonperturbatively
in a regularized setup. Another application is to a small black hole in AdS5*S5
that can evaporate without being attached to a heat bath, for which our
approach suggests a gauge theory origin of the Page curve. The confined degrees
of freedom in the partially-deconfined states play the important roles.
