A Study on the Norms of Toeplitz Matrices with the Generalized Mersenne Numbers
Sevda Aktas *
Department of Mathematics, Art and Science Faculty, Zonguldak B¨ ulent Ecevit University, 67100, Zonguldak, Turkey.
Yuksel Soykan
Department of Mathematics, Art and Science Faculty, Zonguldak B¨ ulent Ecevit University, 67100, Zonguldak, Turkey.
*Author to whom correspondence should be addressed.
Abstract
In this article presents findings related to Toeplitz matrices with Mersenne numbers. We started by creating Toeplitz matrices whose components are Mersenne numbers. We then calculated the Euclidian, row and column norms of these matrices and established both lower and upper bounds for their spectral norms. Additionally, we determined the upper bounds for the Frobenius and spectral norms of the Kronecker and Hadamard product matrices of the Toeplitz matrices with Mersenne numbers.
Keywords: Mersenne numbers, Toeplitz matrix, norm, Hadamard product, Kronecker product