Abstract
The Pell numbers, named after the English diplomat and mathematician John Pell, are studied by many authors. At this work, by inspiring the definition harmonic numbers, we define harmonic Pell numbers. Moreover, we construct one type of symmetric matrix family whose elements are harmonic Pell numbers and its Hadamard exponential matrix. We investigate some linear algebraic properties and obtain inequalities by using matrix norms. Furthermore, some summation identities for harmonic Pell numbers are obtained. Finally, we give a MATLAB-R2016a code which writes the matrix with harmonic Pell entries and calculates some norms and bounds for the Hadamard exponential matrix.
Highlights
The Pell numbers [1] which are defined by the recurrence relation, for n ≥ 0: Its Inversion, Permanents and Some
We have an upper bound for the spectral norm of the matrix e◦P as follow: s ke
We examine some linear algebraic properties of the matrices and state some bounds for the Euclidean and spectral norms of them
Summary
The Pell numbers [1] which are defined by the recurrence relation, for n ≥ 0: Its Inversion, Permanents and Some. In [3], the authors introduce a new type of matrix called circulant-like matrix whose entries are written as functions of Horadam, Fibonacci, Jacobsthal and Pell numbers. Petroudi et al define a special symmetric matrix form and its Hadamard exponential matrix They give inverses and some norms for the matrices, in [18]. We construct a new type of symmetric matrix whose entries are the harmonic Pell numbers and its Hadamard exponential matrix. We present a MATLAB-R2016a code which writes the matrix with harmonic Pell entries and calculates some norms and bounds for the Hadamard exponential matrix
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