Vali-e-Asr university of Rafsanjan Wavelet and Linear Algebra 2383-1936 13 1 2026 07 01 Solving Tensor Equation Systems under the Semi-Tensor Product: A t-Product Approach 1 46 737857 10.22072/wala.2026.2079726.1481 EN Javad Fathi Department of Mathematics, University of hormozgan, Bandarabbas, Iran Journal Article 2025 12 02 This paper addresses the solvability of the tensor system A⋉X = B, X ⋉C = D using the semi-tensor product framework. Initially, we examine the associated tensor-vector system under the semi-tensor product operation, deriving necessary and sufficient conditions for the existence of solutions and propose explicit solution methods. Furthermore, we introduce suitable tensor partitioning techniques that enable the reduction of the tensor-vector system to a linear system formulated via the t-product. This approach facilitates a comprehensive study of the solvability of the tensor system when the unknown tensor X is a vector, matrix or a higher-order tensor under the semi-tensor product. We apply the STP framework to model and control Boolean gene regulatory networks with pinning control inputs. Several illustrative examples are provided to demonstrate the applicability and effectiveness of the proposed approaches. Our study includes the tensor equation A⋉X = B and the matrix system A ⋉ X = B, X ⋉ C = D as special cases.

https://wala.vru.ac.ir/article_737857_877a760a46fbfe56915115e961d95c45.pdf