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Dergiler / Konuralp Journal of Mathematics / 2026 / Volume: 10 Issue: 1

Some Special Matrices with Harmonic Numbers

Seyyed Hossein Jafari Petroudi(Payame Noor University)0000-0003-4127-9215
Maryam Pirouz(Guilan University)
Mücahit Akbıyık(BEYKENT UNIVERSITY)0000-0002-0256-1472
Fatih Yılmaz(Ankara Hacı Bayram Veli Üniversitesi)
Sayfa
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Yayın Tarihi
2022-04-15
DOI
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Finally, we derive some identities about principal minors of these matrices.

📌 3 Maddede Bu Makale

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Amaç & Hipotez: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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Temel Bulgular & Veri:Determinants and inverses of these matrices are investigated.
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Sonuç & Katkı:Finally, we derive some identities about principal minors of these matrices.
🔬Tür:Research Article
📍Kapsam:Genişletilmiş Akademik Örneklem
⚙️Değişkenler: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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Bu Makaleye Atıf Yap

Petroudi, S. H. J., Pirouz, M., Akbıyık, M., Yılmaz, F. (2022). Some Special Matrices with Harmonic Numbers. Konuralp Journal of Mathematics, Volume: 10 Issue: 1. https://ajindex.com/articles/1521583

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