The generalized Levinger transformation

Details The generalized Levinger transformation The generalized Levinger transformation

2007-12-22

arxiv.org/abs/0712.3883v1

Mathematics

Rings and Algebras

8th Workshop on "Numerical Ranges and Numerical Radii" (WONRA), University of Bremen, 2006

Scientific paper

In this paper, we present new results relating the numerical range of a matrix $A$ with generalized Levinger transformation $\mathcal{L}(A,\alpha,\beta) = \alphaH_A +\betaS_A$, where $H_A$ and $S_A$, are respectively the Hermitian and skew-hermitian parts of $A$. Using these results, we derive expressions for eigenvalues and eigenvectors of the perturbed matrix $A + \mathcal{L}(E,\alpha,\beta)$, for a fixed matrix $E$ and $\alpha, \beta$ are real parameters.

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