Some properties of matrix product and its applications in nonnegative tensor decomposition

Some prosperities of matrix product are presented in the paper, Kronecker product, Khatri-Rao product, Hadamard product and outer product are involved. And we get some results that a multilinear tensor can be represented by the product of matrix product for a three order tensor. For higher tensor, we conjure that the same results also hold. By the representation of matrix, we give an iterative algorithm for nonnegative tensor decomposition method which has good convergence performance. Numerical experiments show that our algorithm is effective.