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AI Summary & Key Takeaways
AI Insight⚡ TL;DR(Too Long; Didn't Read)
Finally, we derive some identities about principal minors of these matrices.
📌 3 Key Takeaways
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Objective & Hypothesis:In this paper, we define a particular $n\times n$ matrix $H=[H_{k_{i,j}}]_{i,j=1}^{n}$ and its Hadamard exponential matrix $e^{\circ H}=[e^{H_{k_{i,j}}}]$, where $k_{i,j}=min(i,j)$ and $H_n$ is the $n^{th}$ harmonic number.
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Key Findings & Data:Determinants and inverses of these matrices are investigated.
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Conclusion & Impact:Finally, we derive some identities about principal minors of these matrices.
🔬Design:Research Article
📍Scope:Comprehensive Sample
⚙️Variables:Harmonic number · Spectral norm · Hadamard inverse
Abstract
In this paper, we define a particular $n\times n$ matrix $H=[H_{k_{i,j}}]_{i,j=1}^{n}$ and its Hadamard exponential matrix $e^{\circ H}=[e^{H_{k_{i,j}}}]$, where $k_{i,j}=min(i,j)$ and $H_n$ is the $n^{th}$ harmonic number. Determinants and inverses of these matrices are investigated. Moreover, the Euclidean norm and two upper bounds and lower bounds for the spectral norm of these matrices are presented. Finally, we derive some identities about principal minors of these matrices.
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Cite This Article
PETROUDİ, S. H. J., PİROUZ, M., AKBIYIK, M., YILMAZ, F. (2022). Some Special Matrices with Harmonic Numbers. Konuralp Journal of Mathematics, Cilt: 10 - Sayı: 1, 188–196. https://ajindex.com/articles/786367