On the Norms of Toeplitz Matrices with the Generalized Oresme Numbers
Sevda Aktaş
Department of Mathematics, Faculty of Science, Zonguldak B¨ ulent Ecevit University, Zonguldak-67100, Turkey.
Yüksel Soykan *
Department of Mathematics, Faculty of Science, Zonguldak B¨ ulent Ecevit University, Zonguldak-67100, Turkey.
*Author to whom correspondence should be addressed.
Abstract
In this article, we present results on Toeplitz matrices with Oresme numbers components. First, the Toeplitz matrices with Oresme numbers components are created and then the Frobenius(Euclidian), row and column norms of these matrices are found. Furthermore lower and upper bounds are obtained for the spectral norms of these matrices. In addition, the upper bounds for the Frobenius and spectral norms of the Kronecker and Hadamard product matrices of the Toeplitz matrices with the Oresme numbers are calculated.
Keywords: Oresme numbers, Toeplitz matrix, norm, Hadamard product, Kronecker product