4 Localization of Eigenvalues of Finite Matrices
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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.
KeywordsSpectral Radius Spectral Variation Algebraic Multiplicity Intersecting Line Matching Distance
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