More on semipositive tensor and tensor complementarity problem

TL;DR

This paper investigates properties of semipositive tensors, establishing invariance, necessary and sufficient conditions for semipositivity, and exploring relations with majorization matrices within the context of tensor complementarity problems.

Contribution

It introduces new properties and conditions for semipositive tensors and links between semipositive tensors and their majorization matrices, advancing the theoretical understanding.

Findings

Invariance property of semipositive tensors established.

Necessary and sufficient conditions for semipositivity proved.

Relation between even order row diagonal semipositive tensors and majorization matrices proposed.

Abstract

In recent years several classes of structured matrices are extended to classes of tensors in the context of tensor complementarity problem. The tensor complementarity problem is a class of nonlinear complementarity problem where the involved functions are special polynomials defined by a tensor. Semipositive and strictly semipositive tensors play an important role in the study of the tensor complementarity problem. The article considers some important properties of semipositive tensor. We establish invariance property of semipositive tensor. We prove necessary and sufficient conditions for a tensor to be semipositive tensor. A relation between even order row diagonal semipositive tensor and its majorization matrix is proposed. Keywords: Tensor complementarity problem, semipositive tensor, semimonotone matrix, null vector, majorization matrix.