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Advances in Applied Clifford Algebras

, Volume 26, Issue 4, pp 1095–1125 | Cite as

Bounds for Eigenvalues of Matrix Polynomials Over Quaternion Division Algebra

  • Sk. Safique AhmadEmail author
  • Istkhar Ali
Article

Abstract

Localization theorems are discussed for the left and right eigenvalues of block quaternionic matrices. Basic definitions of the left and right eigenvalues of quaternionic matrices are extended to quaternionic matrix polynomials. Furthermore, bounds on the absolute values of the left and right eigenvalues of quaternionic matrix polynomials are devised and illustrated for the matrix p norm, where \({p = 1, 2, \infty, F}\). The above generalizes the bounds on the absolute values of the eigenvalues of complex matrix polynomials, which give sharper bounds to the bounds developed in [LAA, 358, pp. 5–22 2003] for the case of 1, 2, and \({\infty}\) matrix norms.

Keywords

Skew field Quaternionic matrix Left and right eigenvalues Quaternionic matrix polynomials Quaternionic block companion matrix 

Mathematics Subject Classification

12E15 34L15 15A18 15A66 

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Copyright information

© Springer International Publishing 2016

Authors and Affiliations

  1. 1.School of Basic Sciences, Discipline of MathematicsIndian Institute of Technology IndoreIndoreIndia
  2. 2.School of Basic Sciences, Discipline of MathematicsIndian Institute of Technology IndoreIndoreIndia

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