An overview of relative \(\sin\Theta\) theorems for invariant subspaces of complex matrices (Q1591179)
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scientific article; zbMATH DE number 1546544
| Language | Label | Description | Also known as |
|---|---|---|---|
| English | An overview of relative \(\sin\Theta\) theorems for invariant subspaces of complex matrices |
scientific article; zbMATH DE number 1546544 |
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An overview of relative \(\sin\Theta\) theorems for invariant subspaces of complex matrices (English)
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26 June 2001
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A complex square matrix is assumed to possess an invariant subspace, and a change of this subspace under a perturbation is measured by a certain ``pricipal'' angle. For its sinus, a number of estimates is reviewed/listed for both the additive and multiplicative perturbations and different assumptions about the matrix. The review, a successor of similar surveys, offers another set of explanations why certain high-accuracy diagonalization methods are so reliable. It is well written and well understandable, with both the ideas and technicalities amply illustrated by the three-dimensional or partitioned examples.
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invariant subspace
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rotation by perturbation
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bounds on angle
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dependence on eigenvalues
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grading and scaling
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reliable computation of eigenvectors
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numerical examples
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