  In this paper, we study the stochastic local operation and classical
communication (SLOCC) and local unitary (LU) equivalence for multi-qudit states
by mode-$n$ matricization of the coefficient tensors. We establish a new scheme
of using the CANDECOMP/PARAFAC (CP) decomposition of tensors to find necessary
and sufficient conditions between the mode-$n$ unfolding and SLOCC\&LU
equivalence for pure multi-qudit states. For multipartite mixed states, we
present a necessary and sufficient condition for LU equivalence and necessary
condition for SLOCC equivalence.
