  We study the target space entanglement entropy in a complex matrix model that
describes the chiral primary sector in $\mathcal{N}=4$ super Yang-Mills theory,
which is associated with the bubbling AdS geometry. The target space for the
matrix model is a two-dimensional plane where the eigenvalues of the complex
matrix distribute. The eigenvalues are viewed as the position coordinates of
fermions, and the eigenvalue distribution corresponds to a droplet formed by
the fermions. The droplet is identified with one that specifies a boundary
condition in the bubbling geometry. We consider states in the matrix model that
correspond to $AdS_5\times S^5$, an AdS giant graviton and a giant graviton in
the bubbling geometry. We calculate the target space entanglement entropy of a
subregion for each of the states in the matrix model as well as the area of the
boundary of the subregion in the bubbling geometry, and find a qualitative
agreement between them.
