Mathematics Faculty Articles

Title

Gersgorin Type Theorems for Quaternionic Matrices

Document Type

Article

Publication Date

7-1-2007

Publication Title

Linear Algebra and its Applications

Keywords

Eigenvalue, Geršgorin theorem, Left eigenvalue, Matrix of quaternions, Quaternion, Quaternionic matrix, Right eigenvalue, Singular eigenvalue, Spectral radius, Spectrum

ISSN

0024-3795

Volume

424

Issue/No.

1

First Page

139

Last Page

153

Abstract

This paper aims to set an account of the left eigenvalue problems for real quaternionic (finite) matrices. In particular, we will present the Geršgorin type theorems for the left (and right) eigenvalues of square quaternionic matrices. We shall conclude the paper with examples showing and summarizing some differences between complex matrices and quaternionic matrices and right and left eigenvalues of quaternionic matrices.

Comments

Under an Elsevier user license

DOI

10.1016/j.laa.2006.08.004