Determinants and inverses of circulant matrices with complex Fibonacci numbers

ALTINIŞIK E., Yalcin N. F., BÜYÜKKÖSE Ş.

SPECIAL MATRICES, cilt.3, sa.1, ss.82-90, 2015 (ESCI) identifier identifier

  • Yayın Türü: Makale / Tam Makale
  • Cilt numarası: 3 Sayı: 1
  • Basım Tarihi: 2015
  • Doi Numarası: 10.1515/spma-2015-0008
  • Dergi Adı: SPECIAL MATRICES
  • Derginin Tarandığı İndeksler: Emerging Sources Citation Index (ESCI), Scopus
  • Sayfa Sayıları: ss.82-90
  • Anahtar Kelimeler: Circulant matrix, determinant, complex Fibonacci sequence, Fibonacci sequence
  • Gazi Üniversitesi Adresli: Evet

Özet

Let F-n = circ (F-1*, F-2*,..., F-n*) be the n x n circulant matrix associated with complex Fibonacci numbers F-1*, F-2*,..., F-n*. In the present paper we calculate the determinant of F-n in terms of complex Fibonacci numbers. Furthermore, we show that F-n is invertible and obtain the entries of the inverse of F-n in terms of complex Fibonacci numbers.