Relative perturbation theory for a class of diagonalizable Hermitian matrix pairs (Q1855439)
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scientific article; zbMATH DE number 1864797
| Language | Label | Description | Also known as |
|---|---|---|---|
| English | Relative perturbation theory for a class of diagonalizable Hermitian matrix pairs |
scientific article; zbMATH DE number 1864797 |
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Relative perturbation theory for a class of diagonalizable Hermitian matrix pairs (English)
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5 February 2003
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The author generalizes a result of \textit{K. Veselić} and \textit{I. Slapničar} [Linear Algebra Appl. 195, 81-116 (1993; Zbl 0795.15011)] on relative perturbation of eigenvalues of the Hermitian matrix pair \((H,K)\), by replacing the requirement that \(K\) be positive definite by the weaker requirement that there exists a real polynomial \(p\) such that \(Kp(K^{-1}H)\) is positive definite. Some other related results are also proved.
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relative perturbation
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strongly definitizable matrix pencils
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eigenvalues
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Hermitian matrix pair
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positive definite
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0.9219549
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0.90153813
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