Localization theorems for matrices and bounds for the zeros of polynomials over quaternion division algebra

Author:

Ahmad Sk.1,Ali Istkhar1

Affiliation:

1. Discipline of Mathematics, School of Basic Sciences, Indian Institute of Technology Indore, Simrol, Indore, India

Abstract

In this paper, we derive Ostrowski and Brauer type theorems for the left and right eigenvalues of a quaternionic matrix. Generalizations of Gerschgorin type theorems are discussed for the left and the right eigenvalues of a quaternionic matrix. After that, a sufficient condition for the stability of a quaternionic matrix is given that generalizes the stability condition for a complex matrix. Finally, a characterization of bounds is derived for the zeros of quaternionic polynomials.

Publisher

National Library of Serbia

Subject

General Mathematics

Cited by 4 articles. 订阅此论文施引文献 订阅此论文施引文献,注册后可以免费订阅5篇论文的施引文献,订阅后可以查看论文全部施引文献

1. Bounds for the Zeros of a Quaternionic Polynomial with Restricted Coefficients;Advances in Applied Clifford Algebras;2024-08-07

2. Perturbation analysis of matrices over a quaternion division algebra;ETNA - Electronic Transactions on Numerical Analysis;2021

3. On the Quaternionic Quadratic Equation $$\varvec{xax+bx+xc+d=0}$$;Advances in Applied Clifford Algebras;2019-08-17

4. Location of Right Eigenvalues of Quaternionic Matrix Polynomials;Advances in Applied Clifford Algebras;2019-08-09

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