  We study multipartite entanglement under stochastic local operations and
classical communication (SLOCC) and propose the entanglement classification
under SLOCC for arbitrary-dimensional multipartite ($n$-qudit) pure states via
the rank of coefficient matrix, together with the permutation of qudits. The
ranks of the coefficient matrices have been proved to be entanglement
monotones. The entanglement classification of the $2 \otimes 2 \otimes 2
\otimes 4$ system is discussed in terms of the generalized method, and 22
different SLOCC families are found.
