The Low-Rank Approximation of Fourth-Order Partial-Symmetric and Conjugate Partial-Symmetric Tensor

We present an orthogonal matrix outer product decomposition for the fourth-order conjugate partial-symmetric(CPS)tensor and show that the greedy successive rank-one approximation(SROA)algorithm can recover this decomposition exactly.Based on this matrix decomposition,the CP rank of CPS tensor can be bounded by the matrix rank,which can be applied to low-rank tensor completion.Additionally,we give the rank-one equivalence property for the CPS tensor based on the SVD of matrix,which can be applied to the rank-one approximation for CPS tensors.