  We study the genuine multipartite entanglement in tripartite quantum systems.
By using the Schmidt decomposition and local unitary transformation, we convert
the general states to simpler forms and consider certain matrices from
correlation tensors in the Bloch representation of the simplified density
matrices. Using these special matrices, we obtain new criteria for genuine
multipartite entanglement. Detail examples show that our criteria are able to
detect more tripartite entangled and genuine tripartite entangled states than
some existing criteria.
