Some Special Matrices with Harmonic Numbers
Authors : Seyyed Hossein Jafari Petroudi, Maryam Pirouz, Mücahit Akbiyik, Fatih Yilmaz
Pages : 188-196
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Publication Date : 2022-04-15
Article Type : Research
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.Keywords : Harmonic number, Spectral norm, Hadamard inverse, determinant