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Volume 14
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10.3390/axioms14080609
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Article

Structured Distance to Normality of Dirichlet–Neumann Tridiagonal Toeplitz Matrices

by
Zhaolin Jiang
1,2,
Hongxiao Chu
2,
Qiaoyun Miao
3,* and
Ziwu Jiang
4
1
School of Intelligent Science and Control Engineering, Shandong Vocational and Technical University of International Studies, Rizhao 276800, China
2
School of Mathematics and Statistics, Linyi University, Linyi 276000, China
3
School of Mathematics and Statistics, Qingdao University, Qingdao 266071, China
4
School of Information Science and Engineering, Linyi University, Linyi 276000, China
*
Author to whom correspondence should be addressed.
Axioms 2025, 14(8), 609; https://doi.org/10.3390/axioms14080609
Submission received: 8 July 2025 / Revised: 31 July 2025 / Accepted: 1 August 2025 / Published: 5 August 2025
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Abstract

This paper conducts a rigorous study on the spectral properties and operator-space distances of perturbed Dirichlet–Neumann tridiagonal (PDNT) Toeplitz matrices, with emphasis on their asymptotic behaviors. We establish explicit closed-form solutions for the eigenvalues and associated eigenvectors, highlighting their fundamental importance for characterizing matrix stability in the presence of perturbations. By exploiting the structural characteristics of PDNT Toeplitz matrices, we obtain closed-form expressions quantifying the distance to normality, the deviation from normality.
Keywords: Toeplitz matrix; eigenvalue; normal matrix; distance; Frobenius norm Toeplitz matrix; eigenvalue; normal matrix; distance; Frobenius norm

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MDPI and ACS Style

Jiang, Z.; Chu, H.; Miao, Q.; Jiang, Z. Structured Distance to Normality of Dirichlet–Neumann Tridiagonal Toeplitz Matrices. Axioms 2025, 14, 609. https://doi.org/10.3390/axioms14080609

AMA Style

Jiang Z, Chu H, Miao Q, Jiang Z. Structured Distance to Normality of Dirichlet–Neumann Tridiagonal Toeplitz Matrices. Axioms. 2025; 14(8):609. https://doi.org/10.3390/axioms14080609

Chicago/Turabian Style

Jiang, Zhaolin, Hongxiao Chu, Qiaoyun Miao, and Ziwu Jiang. 2025. "Structured Distance to Normality of Dirichlet–Neumann Tridiagonal Toeplitz Matrices" Axioms 14, no. 8: 609. https://doi.org/10.3390/axioms14080609

APA Style

Jiang, Z., Chu, H., Miao, Q., & Jiang, Z. (2025). Structured Distance to Normality of Dirichlet–Neumann Tridiagonal Toeplitz Matrices. Axioms, 14(8), 609. https://doi.org/10.3390/axioms14080609

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