BOUNDS FOR THE NORMS OF TOEPLITZ MATRICES WITH k-JACOBSTHAL AND kJACOBSTHAL LUCAS NUMBERS

Abstract

This work is concerned with the spectral, Euclid norms of Toeplitz matrices with generalized 𝑘-Jacobsthal and k- Jacobsthal Lucas entries. 𝑘- Jacobsthal and k- Jacobsthal Lucas sequences are twogeneralizations of two very popular special integer sequences called Jacobsthal and Jacobsthal Lucassequences. Upper and lower bounds for the spectral norms of these matrices, that is, the matrices ofthe forms 𝐴 = 𝑇 (𝑗𝑘,0,𝑗𝑘,1, … ,𝑗𝑘,𝑛−1 ) and 𝐵 = 𝑇 (𝑐𝑘,0, 𝑐𝑘,1, … , 𝑐𝑘,𝑛−1 ) are obtained. The upperbounds for the Euclidean and spectral norms of Kronecker and Hadamard product matrices of Toeplitzmatrices with k-Jacobsthal and the k- Jacobsthal Lucas numbers are computed.