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

Abstract

Abstract

On the Norms of RFMLR-Circulant Matrices with the Exponential and Trigonometric Functions

“…Especially, some scholars studied the norms of r-circulant matrices, geometric circulant matrices, and r-Hankel and r-Toeplitz matrices with some famous numbers and polynomials. For example, on the spectral norms of circulant matrices, r-circulant matrices, geometric circulant matrices, and r-Hankel and r-Toeplitz matrices with Fibonacci number, Lucas number, generalized Fibonacci and Lucas numbers, and generalized k-Horadam numbers have been studied [2][3][4][5][6][7][8]. We have obtained several results [9,10] of the norms of matrices mentioned above with exponential forms e(k/n) and trigonometric functions cos(kπ/n) and sin(kπ/n).…”

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].…”