# The low-rank approximation of fourth-order partial-symmetric and conjugate partial-symmetric tensor

@article{Sabir2021TheLA, title={The low-rank approximation of fourth-order partial-symmetric and conjugate partial-symmetric tensor}, author={Amina Sabir and Pegnfei Huang and Qingzhi Yang}, journal={ArXiv}, year={2021}, volume={abs/2111.03238} }

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 rankone equivalence property for the CPS tensor based on the SVD of matrix, which can…

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