The generalized Levinger transformation - Mathematics > Rings and Algebras

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Abstract: In this paper, we present new results relating the numerical range of amatrix $A$ with generalized Levinger transformation$\mathcal{L}A,\alpha,\beta = \alphaH A +\betaS A$, where $H A$ and $S A$, arerespectively the Hermitian and skew-hermitian parts of $A$. Using theseresults, we derive expressions for eigenvalues and eigenvectors of theperturbed matrix $A + \mathcal{L}E,\alpha,\beta$, for a fixed matrix $E$ and$\alpha, \beta$ are real parameters.

Author: M. Adam, J. Maroulas

Source: https://arxiv.org/