Properties of S-tensors

Strict feasibility is an important issue in studies on the theory and algorithms of complementarity problems. For the tensor complementarity problem, strict feasibility can be characterized by the S-tensor. In this paper, we discuss properties of S-tensors. We illustrate that principal sub-tensors of an S-tensor are not always an S-tensor. In particular, we propose several necessary and/or sufficient conditions to judge whether a tensor is an S-tensor or not. Moreover, we also discuss relationship among S-tensors and several related tensors.