On the Norms and Eigenvalues of r -Circulant Matrices with k -Mersenne and k -Mersenne–Lucas Numbers

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Kumari M., Prasad K., ÖZKAN E., Tanti J.

Mathematical Notes, cilt.114, sa.3-4, ss.522-535, 2023 (SCI-Expanded) identifier

  • Yayın Türü: Makale / Tam Makale
  • Cilt numarası: 114 Sayı: 3-4
  • Basım Tarihi: 2023
  • Doi Numarası: 10.1134/s0001434623090225
  • Dergi Adı: Mathematical Notes
  • Derginin Tarandığı İndeksler: Science Citation Index Expanded (SCI-EXPANDED), Scopus, Academic Search Premier, MathSciNet, zbMATH
  • Sayfa Sayıları: ss.522-535
  • Anahtar Kelimeler: eigenvalue, Euclidean norm, k -Mersenne number, k -Mersenne–Lucas number, r -circulant matrix, spectral norm
  • Erzincan Binali Yıldırım Üniversitesi Adresli: Evet

Özet

Abstract: In this work, we study the r -circulant matrix C_r = Circ_r(c_0, c_1,c_2,..,c_{n-1}) such that the entries of C_r are c_i=M_{k,a+ib} or c_i=R_{k,a+ib} , where M_{k,a+ib} and R_{k,a+ib} are k -Mersenne and k -Mersenne–Lucas numbers, respectively. We obtain the eigenvalues and determinants for the matrices and some important identities for the k -Mersenne and k -Mersenne–Lucas numbers. Furthermore, we find norms and bounds estimation for the spectral norm for these r -circulant matrices.