$ SDD_2 $ tensors and $ B_2 $-tensors

Keru Wen; Jiaqi Qi; Yaqiang Wang; Keru Wen; Jiaqi Qi; Yaqiang Wang

doi:10.3934/era.2025108

Electronic Research Archive

2025, Volume 33, Issue 4: 2433-2451. doi: 10.3934/era.2025108

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Research article

$ SDD_2 $ tensors and $ B_2 $-tensors

School of Mathematics and Information Science, Baoji University of Arts and Sciences, Baoji 721013, China

Received: 24 January 2025 Revised: 16 April 2025 Accepted: 16 April 2025 Published: 23 April 2025

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 $ SDD_2 $ tensors, which are derived from $ SDD_2 $ matrices and constitute a subclass of strong $ \mathcal{H} $-tensors. Furthermore, we also investigate the relationships among $ SDD_2 $ tensors, strong $ \mathcal{H} $-tensors, $ SDD_1 $ tensors and $ SDD $ tensors. Additionally, we extend the concept of $ SDD_2 $ tensors to $ B $-tensors, thereby defining a new tensor class called $ B_2 $-tensors and analyzing their fundamental properties.
- $ \mathcal{H} $-tensor,
- $ SDD_2 $ tensor,
- $ B_2 $-tensor,
- real symmetric tensor,
- even-order homogeneous polynomial
Citation: Keru Wen, Jiaqi Qi, Yaqiang Wang. $ SDD_2 $ tensors and $ B_2 $-tensors[J]. Electronic Research Archive, 2025, 33(4): 2433-2451. doi: 10.3934/era.2025108

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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 $ SDD_2 $ tensors, which are derived from $ SDD_2 $ matrices and constitute a subclass of strong $ \mathcal{H} $-tensors. Furthermore, we also investigate the relationships among $ SDD_2 $ tensors, strong $ \mathcal{H} $-tensors, $ SDD_1 $ tensors and $ SDD $ tensors. Additionally, we extend the concept of $ SDD_2 $ tensors to $ B $-tensors, thereby defining a new tensor class called $ B_2 $-tensors and analyzing their fundamental properties.

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