ON BOUNDS FOR THE SMALLEST AND THE LARGEST EIGENVALUES OF GCD AND LCM MATRICES

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ALTINIŞIK E., BÜYÜKKÖSE Ş.

MATHEMATICAL INEQUALITIES & APPLICATIONS, cilt.19, sa.1, ss.117-125, 2016 (SCI-Expanded, Scopus)

  • Yayın Türü: Makale / Tam Makale
  • Cilt numarası: 19 Sayı: 1
  • Basım Tarihi: 2016
  • Doi Numarası: 10.7153/mia-19-09
  • Dergi Adı: MATHEMATICAL INEQUALITIES & APPLICATIONS
  • Derginin Tarandığı İndeksler: Science Citation Index Expanded (SCI-EXPANDED), Scopus
  • Sayfa Sayıları: ss.117-125
  • Anahtar Kelimeler: gcd matrix, lcm matrix, Euler's phi-function, eigenvalue inequalities, trace, Cauchy's interlacing theorem, Rayleigh-Ritz theorem, COMMON DIVISOR MATRICES, JOIN MATRICES, ASYMPTOTIC-BEHAVIOR, TRACES, DETERMINANT, CONJECTURE, PROOF
  • Açık Arşiv Koleksiyonu: AVESİS Açık Erişim Koleksiyonu
  • Gazi Üniversitesi Adresli: Evet

Özet

In this paper, improving a famous result of Wolkowicz and Styan for the GCD matrix (S-n) and the LCM matrix [S-n] defined on S-n = {1,2,..., n}, we present new upper and lower bounds for the smallest and the largest eigenvalues of (S-n) and [S-n] in terms of particular arithmetical functions.