ON THE NORMS OF CIRCULANT MATRICES WITH THE COMPLEX FIBONACCI AND LUCAS NUMBERS

Authors : Süleyman Solak, Mustafa Bahşi

Pages : 487-490

View : 18 | Download : 7

Publication Date : 2016-06-21

Article Type : Conference Paper

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