  This article considers the recovery of low-rank matrices via a convex
nuclear-norm minimization problem and presents two null space properties (NSP)
which characterize uniform recovery for the case of block-diagonal matrices and
block-diagonal positive semidefinite matrices. These null-space conditions turn
out to be special cases of a new general setup, which allows to derive the
mentioned NSPs and well-known NSPs from the literature. We discuss the relative
strength of these conditions and also present a deterministic class of matrices
that satisfies the block-diagonal semidefinite NSP.
