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We solve the entanglement classification under stochastic local operationsand classical communication (SLOCC) for general n-qubit states. For twoarbitrary pure n-qubit states connected via local operations, we establish anequation between the two coefficient matrices associated with the states. Therank of the coefficient matrix is preserved under SLOCC and gives rise to asimple way of partitioning all the pure states of n qubits into differentfamilies of entanglement classes, as exemplified here. When applied to thesymmetric states, this approach reveals that all the Dicke states |l,n> withl=1, ..., [n/2] are inequivalent under SLOCC.

Classification of general n-qubit states under stochastic local operations and classical communication in terms of the rank of coefficient matrix