  The detection and estimation of quantum entanglement are the essential issues
in the theory of quantum entanglement. We construct matrices based on the
realignment of density matrices and the vectorization of the reduced density
matrices, from which a family of separability criteria are presented for both
bipartite and multipartite systems. Moreover, new lower bounds of concurrence
and convex-roof extended negativity are derived. Criteria are also given to
detect the genuine tripartite entanglement. Lower bounds of the concurrence of
genuine tripartite entanglement are presented. By detailed examples we show
that our results are better than the corresponding ones in identifying and
estimating quantum entanglement as well as genuine multipartite entanglement.
