- Gazi University Journal of Science
- Vol: 29 Issue: 2
- ON THE NORMS OF CIRCULANT MATRICES WITH THE COMPLEX FIBONACCI AND LUCAS NUMBERS
ON THE NORMS OF CIRCULANT MATRICES WITH THE COMPLEX FIBONACCI AND LUCAS NUMBERS
Authors : Süleyman Solak, Mustafa Bahşi
Pages : 487-490
View : 9 | Download : 6
Publication Date : 2016-06-20
Article Type : Other
Abstract :In this paper, we compute the norms of circulant matrices with the complex Fibonacci and Lucas numbers. Moreover, we give golden ratio in complex Fibonacci numbers. In some scientific areas such as signal processing, coding theory and image processing, we often encounter circulant matrices. An n n matrix C is called a circulant matrix if it is of the form 0 1 1 1 0 2 2 1 3 1 2 0 n n n n n n c c c c c c C c c c c c c or an n n matrix C is circulant if there exist 0 1 1 , , , n c c c such that the i, j entry of C is j i n mod c , where the rows and columns are numbered from 0 to n 1 and kmodn means the number between 0 to n 1 that is congruent to kmodn. Thus, we denote the circulant matrix C as C Circ c c c 0 1 1 , , , n . Any circulant matrix has many elegant properties. Some of them are [6,12]Keywords : Circulant matrix, Complex Fibonacci numbers, Matrix norm.