One type of symmetric matrix with harmonic pell entries, its inversion, permanents and some norms

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Akbiyik S. Y., Akbiyik M., YILMAZ F.

Mathematics, vol.9, no.5, pp.1-15, 2021 (SCI-Expanded) identifier identifier

  • Publication Type: Article / Article
  • Volume: 9 Issue: 5
  • Publication Date: 2021
  • Doi Number: 10.3390/math9050539
  • Journal Name: Mathematics
  • Journal Indexes: Science Citation Index Expanded (SCI-EXPANDED), Scopus, Aerospace Database, Communication Abstracts, Metadex, zbMATH, Directory of Open Access Journals, Civil Engineering Abstracts
  • Page Numbers: pp.1-15
  • Keywords: harmonic pell number, spectral norm, hadamard inverse, permanent, determinant
  • Ankara Haci Bayram Veli University Affiliated: No

Abstract

© 2021 by the authors. Licensee MDPI, Basel, Switzerland.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.