BOUNDS FOR THE NORMS OF TOEPLITZ MATRICES WITH k-JACOBSTHAL AND k-JACOBSTHAL 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 two generalizations of two very popular special integer sequences called Jacobsthal and Jacobsthal Lucas sequences. Upper and lower bounds for the spectral norms of these matrices, that is, the matrices of the forms 𝐴=𝑇 (𝑗𝑘,0 ,𝑗𝑘,1 ,…,𝑗𝑘,𝑛−1 ) and 𝐵=𝑇 (𝑐𝑘,0 ,𝑐𝑘,1 ,…,𝑐𝑘,𝑛−1 ) are obtained. The upper bounds for the Euclidean and spectral norms of Kronecker and Hadamard product matrices of Toeplitz matrices with k-Jacobsthal and the k- Jacobsthal Lucas numbers are computed.