Some systems of tensor equations under t-product and their applications

Shao-Wen Yu, Wei-Lu Qin, Zhuo-Heng He


In this paper, some systems of tensor equations under t-product are considered. Some practical necessary and sufficient conditions for the existence of a solution to two systems of tensor equations in terms of the Moore-Penrose inverses are given. The general solutions to the systems of tensor equations are presented when they are solvable. An application of the tensor equations in the solvability conditions and general symmetric solution to a system of tensor equations. Some algorithms and numerical examples are provided to illustrate the main results.


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