Solving the two-dimensional CIS problem by a rational algorithm

The CIS problem is formulated as follows. Let p be a fixed integer, 1⩽p<n. For given n×n compex matrices A and B, can one verify whether A and B have a common invariant subspace of dimension p by a procedure employing a finite number of arithmetical operations? We describe an algorithm solving th...

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Bibliographic Details
Published inLinear algebra and its applications Vol. 312; no. 1; pp. 115 - 123
Main Authors Al'pin, Yurii A., George, Alan, Ikramov, Khakim D.
Format Journal Article
LanguageEnglish
Published Elsevier Inc 15.06.2000
Subjects
2-generated matrix algebra
Common invariant subspace
Radical
Rational algorithm
Shemesh's theorem
Socle
Common invariant subspace
Rational algorithm
2-generated matrix algebra
Shemesh's theorem
Socle
Radical
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ISSN0024-3795
1873-1856
DOI10.1016/S0024-3795(00)00098-7

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Summary:The CIS problem is formulated as follows. Let p be a fixed integer, 1⩽p<n. For given n×n compex matrices A and B, can one verify whether A and B have a common invariant subspace of dimension p by a procedure employing a finite number of arithmetical operations? We describe an algorithm solving the CIS problem for p=2. Unlike the algorithm proposed earlier by the second and third authors, the new algorithm does not impose any restrictions 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.
ISSN:0024-3795
1873-1856
DOI:10.1016/S0024-3795(00)00098-7