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<p>In this paper, we study the C-eigenvalue via the tensor C-product. Definitions of the C-eigenvalue and Hermitian tensor are proposed. We also present the C-Jordan canonical form of the third-order F-square tensors and a commutative tensor family based on the C-product. Then, we prove some C-eigenvalues inequalities for Hermitian tensors, including extensions of Weyl’s theorem and Cauchy’s interlacing theorem from the matrix case to the tensor case. Finally, we introduce the stability of the C-eigenvalues and study the Lyapunov equation for tensors.</p>

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A study on the C-eigenvalue of the third-order tensors

  • 期刊论文

  • 发表日期：

    2025年1月6日

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  • Jie Liu,
  • Xiaoji Liu,
  • Hongwei Jin,
  • Hongxing Wang

摘要

In this paper, we study the C-eigenvalue via the tensor C-product. Definitions of the C-eigenvalue and Hermitian tensor are proposed. We also present the C-Jordan canonical form of the third-order F-square tensors and a commutative tensor family based on the C-product. Then, we prove some C-eigenvalues inequalities for Hermitian tensors, including extensions of Weyl’s theorem and Cauchy’s interlacing theorem from the matrix case to the tensor case. Finally, we introduce the stability of the C-eigenvalues and study the Lyapunov equation for tensors.