Solution Analysis of Tensor Equation $\mathcal{A} \ltimes \mathcal{X} \ltimes \mathcal{B}= \mathcal{C}$ via Semi Tensor Product with t-product

Bhawna Garg; Ranjan Kumar Das

paper

Solution Analysis of Tensor Equation $A ⋉ X ⋉ B = C$ via Semi Tensor Product with t-product

arXiv:2607.07006

Abstract

This paper focuses on the analysis of the tensor equation $A ⋉ X ⋉ B = C$ , formulated via the semi tensor product with t-product. For the unknown vector $X$ , we establish a necessary and sufficient condition that provides an equivalence criterion for the existence of solutions. For matrix valued and higher-order tensor valued unknown $X$ , solvability is determined by corresponding compatibility requirements. Moreover, the explicit structure (Toeplitz and Circulant) of $C$ is characterized. The derived results are supported by several illustrative examples.

23 pages, 1 figure

Solution Analysis of Tensor Equation A⋉X⋉B=C via Semi Tensor Product with t-product

Abstract

Solution Analysis of Tensor Equation $A ⋉ X ⋉ B = C$ via Semi Tensor Product with t-product