4 Localization of Eigenvalues of Finite Matrices

  • Michael I. Gil’
Part of the Lecture Notes in Mathematics book series (LNM, volume 1830)


The present chapter is concerned with perturbations of finite matrices and bounds for their eigenvalues. In particular, we improve the classical Gershgorin result for matrices, which are ”close” to triangular ones. In addition, we derive upper and lower estimates for the spectral radius. Under some restrictions, these estimates improve the Frobenius inequalities. Moreover, we present new conditions for the stability of matrices, which supplement the Rohrbach theorem.


Spectral Radius Spectral Variation Algebraic Multiplicity Intersecting Line Matching Distance 
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Copyright information

© Springer-Verlag Berlin Heidelberg 2003

Authors and Affiliations

  • Michael I. Gil’
    • 1
  1. 1.Department of MathematicsBen Gurion University of NegevBeer-ShevaIsrael

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