The generalized Levinger transformation

Authors:
M. Adam;J. Maroulas
Affiliations:
Department of Computer Science and Biomedical Informatics, University of Central Greece, Lamia 35100, Greece;Department of Mathematics, National Technical University, Zografou Campus, Athens 15780, Greece
Venue:
Journal of Computational and Applied Mathematics
Year:
2010

Citing 3
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Topics in matrix analysis

Topics in matrix analysis
On multiple eigenvalues of matrices depending on several parameters

SIAM Journal on Numerical Analysis
Numerical Linear Algebra and Applications, Second Edition

Numerical Linear Algebra and Applications, Second Edition

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Abstract

In this paper, we present new results relating the numerical range of a matrix A with the generalized Levinger transformation L(A,@a,@b)=@aH"A+@bS"A, where H"A and S"A, are, respectively the Hermitian and skew-Hermitian parts of A. Using these results, we then derive expressions for eigenvalues and eigenvectors of the perturbed matrix A+L(E,@a,@b), for a fixed matrix E and @a, @b are real parameters.