PERTURBATION ANALYSIS OF MATRICES OVER A QUATERNION DIVISION ALGEBRA

被引：5

作者：

Ahmad, S. K. Safique ^{[1
]}

Ali, Istkhar ^{[2
]}

Slapnicar, Ivan ^{[3
]}

机构：

[1] Indian Inst Technol Indore, Dept Math, Khandwa Rd, Indore 453552, Madhya Pradesh, India

[2] Integral Univ, Dept Math & Stat, Kursi Rd, Lucknow 226026, Uttar Pradesh, India

[3] Univ Split, Fac Elect Engn Mech Engn & Naval Architecture, Rudjera Boskovica 32, Split 21000, Croatia

来源：

ELECTRONIC TRANSACTIONS ON NUMERICAL ANALYSIS | 2021年 / 54卷

关键词：

left eigenvalues; right eigenvalues; quaternionic polynomials; Bauer-Fike theorem; quaternionic companion matrices; quaternionic matrix norms; quaternionic matrices; POLYNOMIALS; ZEROS; BOUNDS; EIGENVALUES; ABSOLUTE;

D O I：

10.1553/etna_vol54s128

中图分类号：

O29 [应用数学];

学科分类号：

070104 ;

摘要：

In this paper, we present the concept of perturbation bounds for the right eigenvalues of a quaternionic matrix. In particular, a Bauer-Fike-type theorem for the right eigenvalues of a diagonalizable quaternionic matrix is derived. In addition, perturbations of a quaternionic matrix are discussed via a block-diagonal decomposition and the Jordan canonical form of a quaternionic matrix. The location of the standard right eigenvalues of a quaternionic matrix and a sufficient condition for the stability of a perturbed quaternionic matrix are given. As an application, perturbation bounds for the zeros of quaternionic polynomials are derived. Finally, we give numerical examples to illustrate our results.

引用

页码：128 / 149

页数：22

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