Abstract
The goal of this paper is to investigate a class of linear complementarity problems over tensor-spaces, denoted by TLCP, which is an extension of the classical linear complementarity problem. First, two classes of structured tensors over tensor-spaces (i.e., T-R tensor and T-RO tensor) are introduced and some equivalent characterizations are discussed. Then, the lower bound of the solutions in the sense of the infinity norm of the TLCP is obtained when the problem has a solution. Moreover, by introducing a new quantity, the upper bound of the solutions in the sense of the infinity norm of the TLCP is given when the tensor involved in the problem is a T-RO tensor.
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