Journal of the
Korean Mathematical Society JKMS

In this paper, we suggest a new method for a given tensor to find CP decompositions using a less number of rank $1$ tensors. The main ingredient is the Least Absolute Shrinkage and Selection Operator (LASSO) by considering the decomposition problem as a sparse optimization problem. As applications, we design experiments to find some CP decompositions of the matrix multiplication and determinant tensors. In particular, we find a new formula for the $4 \times 4$ determinant tensor as a sum of $12$ rank $1$ tensors.

Keywords: CP decomposition, tensor rank, LASSO, determinant

MSC numbers: Primary 14N07, 15A15, 62J07

Supported by: J.-H. J. and Y. K. are supported by the Basic Science Program of the NRF of Korea (NRF-2022R1C1C1010052). J.-H. J. participated the introductory school of AGATES in Warsaw (Poland) and thanks the organizers for providing a good research environment throughout the school.