The closure property of H $\mathcal{H}$ -tensors under the Hadamard product

• Main Authors: Lixin Zhou, Jianzhou Liu, Li Zhu
• Format: Article
• Language: English
• Published: SpringerOpen 2017-09-01
• Series: Journal of Inequalities and Applications
• Subjects: H $\mathcal{H}$ -tensors; M $\mathcal{M}$ -tensors; Hadamard product; eigenvalues
• Online Access: http://link.springer.com/article/10.1186/s13660-017-1499-4
• ISSN: 1029-242X

Abstract In this paper, we investigate the closure property of H $\mathcal {H}$ -tensors under the Hadamard product. It is shown that the Hadamard products of Hadamard powers of strong H $\mathcal{H}$ -tensors are still strong H $\mathcal{H}$ -tensors. We then bound the minimal real eigenvalues of the comparison tensors of the Hadamard products involving strong H $\mathcal{H}$ -tensors. Finally, we show how to attain the bounds by characterizing these H $\mathcal{H}$ -tensors.