TOWARD SPECIAL SYMMETRIC MATRICES WITH HARMONIC NUMBERS

In this note a particular symmetric matrix H =(...)where(...) and Hn is the nthHarmonic number is considered. Then we construct its Hadamard exponential matrix e◦H = [e(...)Determinant and leading principal minors of these matrices are investigated. We show that these matricesare invertible and we establish their inversions. Moreover Euclidean norm of H and some bounds for thespectral norm of these matrices are derived. Finally other properties of these matrices are represented.