Improving the localization of eigenvalues for complex matrices (Q2898532)
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scientific article; zbMATH DE number 6054566
| Language | Label | Description | Also known as |
|---|---|---|---|
| English | Improving the localization of eigenvalues for complex matrices |
scientific article; zbMATH DE number 6054566 |
Statements
11 July 2012
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eigenvalues
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spectrum
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localization
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rectangular regions
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Improving the localization of eigenvalues for complex matrices (English)
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Let \(\lambda_i, i= 1,\dots,n\) denote the spectrum of a complex \(n\)-by-\(n\) matrix \(A\). Several well-known bounds for \(\sum|\lambda_i|^2\) in terms of \(\mathrm{tr}(A), \|A\|, \|AA^*-A^*A\|\) are stated. Generalizations to \(\mathrm{Re}(A)\) and \(\mathrm{Im}(A)\) lead to rectangles containing the spectrum of \(A\). Two examples of order 3 are given.
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