Abstract
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.
Keywords
- Spectral Radius
- Spectral Variation
- Algebraic Multiplicity
- Intersecting Line
- Matching Distance
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© 2003 Springer-Verlag Berlin Heidelberg
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Gil’, M.I. (2003). 4 Localization of Eigenvalues of Finite Matrices. In: Operator Functions and Localization of Spectra. Lecture Notes in Mathematics, vol 1830. Springer, Berlin, Heidelberg. https://doi.org/10.1007/978-3-540-45225-6_4
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DOI: https://doi.org/10.1007/978-3-540-45225-6_4
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Publisher Name: Springer, Berlin, Heidelberg
Print ISBN: 978-3-540-20246-2
Online ISBN: 978-3-540-45225-6
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