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Selected Works of Fuzhen Zhang
Article
Gersgorin Type Theorems for Quaternionic Matrices
Linear Algebra and its Applications
  • Fuzhen Zhang, Nova Southeastern University; Shenyang Normal University
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Document Type
Article
Publication Date
7-1-2007
Keywords
  • Eigenvalue,
  • Geršgorin theorem,
  • Left eigenvalue,
  • Matrix of quaternions,
  • Quaternion,
  • Quaternionic matrix,
  • Right eigenvalue,
  • Singular eigenvalue,
  • Spectral radius,
  • Spectrum
Disciplines
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.

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DOI
10.1016/j.laa.2006.08.004
Citation Information
Fuzhen Zhang. "Gersgorin Type Theorems for Quaternionic Matrices" Linear Algebra and its Applications Vol. 424 Iss. 1 (2007) p. 139 - 153 ISSN: 0024-3795
Available at: http://works.bepress.com/fuzhen-zhang/48/