On norms, spread, characteristic polynomial and determinant of Hankel and Toeplitz matrices with Mersenne sequence

Document Type : Original paper

Authors

1 Department of Applied Science and Humanities (Mathematics), Government Engineering College Bhojpur, Bihar, India, 802301

2 Department of Mathematics, Babasaheb Bhimrao Ambedkar University, Lucknow, India, 226025

Abstract

In this work, some new properties of the Hankel and Toeplitz matrices are obtained by considering the Mersenne numbers as entries. We developed efficient formulas to compute matrix norms like .1,  ., Euclidean norm, spread, and the lower and upper bound for the spectral norm of these matrices. Also, the study shows that these matrices are non-singular for n=2 and singular for n3. Furthermore, we presented rank, eigenvalues, principal minors, and the characteristic polynomial of them explicitly.

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Main Subjects


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