  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 on the rank-one
approximation for CPS tensors.
