S DD₂ tensors and B₂-tensors

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Abstract

Strong $\mathcal{H}$-tensors have many important applications in practical problems. In particular, strong $\mathcal{H}$-tensors play an important role in the positive qualitative determination of multivariate even-order homogeneous polynomials. Therefore, research in this field is of great theoretical and practical value. This paper focuses on introducing a novel class of tensors, termed S DD₂ tensors, which are derived from S DD₂ matrices and constitute a subclass of strong $\mathcal{H}$-tensors. Furthermore, we also investigate the relationships among S DD₂ tensors, strong $\mathcal{H}$-tensors, S DD₁ tensors and S DD tensors. Additionally, we extend the concept of S DD₂ tensors to B-tensors, thereby defining a new tensor class called B₂-tensors and analyzing their fundamental properties.

Keywords

$\mathcal{H}$-tensor / S DD₂ tensor / B₂-tensor / real symmetric tensor / even-order homogeneous polynomial

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