On the spectral norm of r-circulant matrices with the Pell and Pell-Lucas numbers

Abstract

Let us define A = C r (a 0 , a 1 , . . . , a n-1 ) to be a n × n r-circulant matrix. The entries in the first row of A = C r (a 0 , a 1 , . . . , a n-1 ) are(i = 0, 1, 2, . . . , n -1), where P i and Q i are the ith Pell and Pell-Lucas numbers, respectively. We find some bounds estimation of the spectral norm for r-Circulant matrices with Pell and Pell-Lucas numbers.

A New Method of Matrix Decomposition to Get the Determinants and Inverses of r -Circulant Matrices with Fibonacci and Lucas Numbers

“…Hong and Jing [18] investigate the invertibility of the Tribonacci r-circulant matrix and show the determinant and the inverse matrix based on constructing the transformation matrices. He et al [19] and Türkmen and Gökbas [20] study the spectral norm of r-circulant matrices with Fibonacci and Lucas numbers and Pell and Pell-Lucas numbers, respectively. When certain circulant matrices having k ones and k + 1 zeros in the first row are nonsingular, Chen [21] proves the conditions which nonsingular matrices satisfy.…”

On The Norms of Another Form of $r-$Circulant Matrices with The Hyper-Fibonacci and Lucas Numbers

“…The circulant matrices and r−circulant matrices have been scientific research area in the recent past decades. Especially, the norms of circulant matrices with special elements such as Fibonacci or Fibonacci like numbers have been investigated extensively [2,3,5,6,[15][16][17][18][19][21][22][23][24][25]. Shen and Cen [21] derived upper and lower bounds for the spectral norms of r-circulant matrices in the forms A = C r (F 0 , F 1 , .…”

“…Tuglu and Kızılateş [18] studied norms of circulant and r−circulant matrices involving harmonic Fibonacci and hyperharmonic Fibonacci numbers. Türkmen and Gökbaş [24] found some bound estimations for the spectral norm of r−circulant matrices with Pell and Pell-Lucas numbers. In [5], the authors computed spectral norms of circulant matrices in the forms…”

On the Norms of <i>r</i>-Hankel Matrices Involving Fibonacci and Lucas Numbers

“…Solak has studied the norms of circulant matrices with fibonacci and lucas numbers in [1], Türkmen and Gökbaş have made a similar study by using the r-circulant matrix with pell and pell-lucas numbers in [2], Shen and Cen have made a similar study by using the same special matrix with k-fibonacci and k-lucas numbers in [3], Akbulak and Bozkurt found lower and upper bounds for the spectral norms of toeplitz matrices with classical fibonacci and lucas numbers entries in [4], Shen gave upper and lower bounds for the spectral norms of toeplitz matrices with k-fibonacci and k-lucas numbers entries in [5], Akbulak and Bozkurt have made a similar study by using the hankel matrix with fibonacci and lucas numbers in [6], Gökbaş and Türkmen gave upper and lower bounds for the spectral norms of r-toeplitz matrices involving fibonacci and lucas numbers in [7], Bozkurt and Tam obtained determinants and inverse of circulant matrices with jacobsthal and jacobsthal-lucas numbers in [8].…”