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One Type of Symmetric Matrix with Harmonic Pell Entries, Its Inversion, Permanents and Some Norms

Author

Listed:
  • Seda Yamaç Akbiyik

    (Department of Computer Engineering, Istanbul Gelisim University, 34310 Istanbul, Turkey
    These authors contributed equally to this work.)

  • Mücahit Akbiyik

    (Department of Mathematics, Beykent University, 34520 Istanbul, Turkey
    These authors contributed equally to this work.)

  • Fatih Yilmaz

    (Department of Mathematics, Ankara Hacı Bayram Veli University, 06900 Ankara, Turkey
    These authors contributed equally to this work.)

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.

Suggested Citation

  • Seda Yamaç Akbiyik & Mücahit Akbiyik & Fatih Yilmaz, 2021. "One Type of Symmetric Matrix with Harmonic Pell Entries, Its Inversion, Permanents and Some Norms," Mathematics, MDPI, vol. 9(5), pages 1-15, March.
    • Handle: RePEc:gam:jmathe:v:9:y:2021:i:5:p:539-:d:510457
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    Cited by:

    1. Fatih Yılmaz & Aybüke Ertaş & Jiteng Jia, 2022. "On Harmonic Complex Balancing Numbers," Mathematics, MDPI, vol. 11(1), pages 1-15, December.

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