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

journal of physics. a, mathematical and theoretical

Classification of arbitrary-dimensional multipartite pure states under  stochastic local operations and classical communication using the rank of  coefficient matrix