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Journals / Hacettepe Journal of Mathematics and Statistics / 2026 / Volume: 50 Issue: 4

Sturm theorem for the generalized Frank matrix

Efruz Özlem Mersin(AKSARAY UNIVERSITY)0000-0001-6260-9063
Mustafa Bahşi(AKSARAY UNIVERSITY)0000-0002-6356-6592
Pages
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Publication Date
2021-08-06
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AI Summary & Key Takeaways

AI Insight
⚡ TL;DR(Too Long; Didn't Read)

Moreover, we illustrate our results with an example.

📌 3 Key Takeaways

🎯
Objective & Hypothesis:One of the popular test matrices for eigenvalue routines is the Frank matrix due to its well-conditioned and poorly conditioned eigenvalues.
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Key Findings & Data:All the eigenvalues of the Frank matrix are real, positive and different.
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Conclusion & Impact:Moreover, we illustrate our results with an example.
🔬Design:Research Article
📍Scope:Comprehensive Sample
⚙️Variables:Sturm Sequence · Characteristic Polynomial · Eigenvalue

Abstract

One of the popular test matrices for eigenvalue routines is the Frank matrix due to its well-conditioned and poorly conditioned eigenvalues. All the eigenvalues of the Frank matrix are real, positive and different. Sturm Theorem is a very useful tool for computing the eigenvalues of tridiagonal symmetric matrices. In this paper, we apply Sturm Theorem to the generalized Frank matrix which is a special form of the Hessenberg matrix and examine its eigenvalues by using Sturm property. Moreover, we illustrate our results with an example.

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Cite This Article

Mersin, E. Ö., Bahşi, M. (2021). Sturm theorem for the generalized Frank matrix. Hacettepe Journal of Mathematics and Statistics, Volume: 50 Issue: 4. https://doi.org/10.15672/hujms.773281

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