On the Norms and Eigenvalues of r -Circulant Matrices with k -Mersenne and k -Mersenne–Lucas Numbers

Abstract: In this work, we study the r -circulant matrix C_r = Circ_r(c_0, c_1,c_2,..,c_{n-1}) such that the entries of C_r are c_i=M_{k,a+ib} or c_i=R_{k,a+ib} , where M_{k,a+ib} and R_{k,a+ib} are k -Mersenne and k -Mersenne–Lucas numbers, respectively. We obtain the eigenvalues and determinants for the matrices and some important identities for the k -Mersenne and k -Mersenne–Lucas numbers. Furthermore, we find norms and bounds estimation for the spectral norm for these r -circulant matrices. © 2023, Pleiades Publishing, Ltd.