Some Special Matrices with Harmonic Numbers

Authors : Seyyed Hossein JAFARİ PETROUDİ, Maryam PİROUZ, Mücahit AKBIYIK, Fatih YILMAZ

Pages : 188-196

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Publication Date : 2022-04-15

Article Type : Research Paper

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 $k_{i,j}=mininsert ignore into journalissuearticles values(i,j);$ 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.
Keywords : Harmonic number, Spectral norm, Hadamard inverse, determinant