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<p>In this paper, we introduce symmetric positive subdefinite tensors as an extension of symmetric positive semidefinite tensors. We investigate the underlying properties of these tensors and establish the equivalence of symmetric positive subdefinite and positive semidefinite tensors under an additional condition. Inspired by Martos’ research on positive subdefinite matrices, we propose a complete characterization of symmetric positive subdefinite tensors of rank one.</p>

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Symmetric positive subdefinite tensors

  • 期刊论文

  • 发表日期：

    2025年5月20日

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  • Sonali Sharma,
  • R. Deb,
  • A. K. Das

摘要

In this paper, we introduce symmetric positive subdefinite tensors as an extension of symmetric positive semidefinite tensors. We investigate the underlying properties of these tensors and establish the equivalence of symmetric positive subdefinite and positive semidefinite tensors under an additional condition. Inspired by Martos’ research on positive subdefinite matrices, we propose a complete characterization of symmetric positive subdefinite tensors of rank one.