Solving the two-dimensional CIS problem by a rational algorithm (Q1573665)
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scientific article; zbMATH DE number 1485560
| Language | Label | Description | Also known as |
|---|---|---|---|
| English | Solving the two-dimensional CIS problem by a rational algorithm |
scientific article; zbMATH DE number 1485560 |
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Solving the two-dimensional CIS problem by a rational algorithm (English)
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26 June 2001
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The common invariant subspace (CIS) problem is discussed. Let \(1\leq p< n\) be a fixed integer, and \(A\) and \(B\) are complex matrices. Can one verify whether \(A\) and \(B\) have a common invariant subspace of dimension \(p\) in a finite number of steps? An algorithm is given which solves the problem for \(p=2\). No restrictions are imposed on \(A\) and \(B\). Moreover, when \(A\) and \(B\) generate a semisimple algebra, the algorithm is able to solve the CIS problem for any \(p, 1<p<n\).
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common invariant subspace
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rational algorithm
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2-generated matrix algebra
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radical
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socle
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Shemesh's theorem
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0.8443616
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0.83664596
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0.82976884
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0.82762295
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0.8255997
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0.8255838
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