A novel procedure for constructing invariant subspaces of a set of matrices
<p>A problem that is frequently encountered in a variety of mathematical contexts is to find the common invariant subspaces of a single or of a set of matrices. A new method is proposed that gives a definitive answer to this problem. The key idea consists of finding common eigenvectors for ext...
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| مؤلفون آخرون: | , , |
| منشور في: |
2022
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| _version_ | 1864513567951159296 |
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| author | Ahmad Y. Al-Dweik (14158875) |
| author2 | Ryad Ghanam (14150847) Gerard Thompson (10116742) Hassan Azad (14150850) |
| author2_role | author author author |
| author_facet | Ahmad Y. Al-Dweik (14158875) Ryad Ghanam (14150847) Gerard Thompson (10116742) Hassan Azad (14150850) |
| author_role | author |
| dc.creator.none.fl_str_mv | Ahmad Y. Al-Dweik (14158875) Ryad Ghanam (14150847) Gerard Thompson (10116742) Hassan Azad (14150850) |
| dc.date.none.fl_str_mv | 2022-11-22T21:12:46Z |
| dc.identifier.none.fl_str_mv | 10.1007/s10231-022-01233-7 |
| dc.relation.none.fl_str_mv | https://figshare.com/articles/journal_contribution/A_novel_procedure_for_constructing_invariant_subspaces_of_a_set_of_matrices/21597156 |
| dc.rights.none.fl_str_mv | CC BY 4.0 info:eu-repo/semantics/openAccess |
| dc.subject.none.fl_str_mv | Applied mathematics Applied Mathematics |
| dc.title.none.fl_str_mv | A novel procedure for constructing invariant subspaces of a set of matrices |
| dc.type.none.fl_str_mv | Text Journal contribution info:eu-repo/semantics/publishedVersion text contribution to journal |
| description | <p>A problem that is frequently encountered in a variety of mathematical contexts is to find the common invariant subspaces of a single or of a set of matrices. A new method is proposed that gives a definitive answer to this problem. The key idea consists of finding common eigenvectors for exterior powers of the matrices concerned. A convenient formulation of the Plücker relations is then used to ensure that these eigenvectors actually correspond to subspaces or provide the initial constraints for eigenvectors involving parameters. A procedure for computing the divisors of a totally decomposable vector is also provided. Several examples are given for which the calculations are too tedious to do by hand and are performed by coding the conditions found into Maple. Our main motivation lies in Lie symmetry, where the invariant subspaces of the adjoint representations for the Lie symmetry algebra of a differential equation must be known explicitly and comprehensively in order to determine all the ideals of the Lie symmetry algebra.</p><h2>Other Information</h2> <p> Published in: Annali di Matematica Pura ed Applicata (1923 -)<br> License: <a href="https://creativecommons.org/licenses/by/4.0" target="_blank">https://creativecommons.org/licenses/by/4.0</a><br>See article on publisher's website: <a href="http://dx.doi.org/10.1007/s10231-022-01233-7" target="_blank">http://dx.doi.org/10.1007/s10231-022-01233-7</a></p> |
| eu_rights_str_mv | openAccess |
| id | Manara2_5240c80b0c40d257bc25d8149e9b48bf |
| identifier_str_mv | 10.1007/s10231-022-01233-7 |
| network_acronym_str | Manara2 |
| network_name_str | Manara2 |
| oai_identifier_str | oai:figshare.com:article/21597156 |
| publishDate | 2022 |
| repository.mail.fl_str_mv | |
| repository.name.fl_str_mv | |
| repository_id_str | |
| rights_invalid_str_mv | CC BY 4.0 |
| spelling | A novel procedure for constructing invariant subspaces of a set of matricesAhmad Y. Al-Dweik (14158875)Ryad Ghanam (14150847)Gerard Thompson (10116742)Hassan Azad (14150850)Applied mathematicsApplied Mathematics<p>A problem that is frequently encountered in a variety of mathematical contexts is to find the common invariant subspaces of a single or of a set of matrices. A new method is proposed that gives a definitive answer to this problem. The key idea consists of finding common eigenvectors for exterior powers of the matrices concerned. A convenient formulation of the Plücker relations is then used to ensure that these eigenvectors actually correspond to subspaces or provide the initial constraints for eigenvectors involving parameters. A procedure for computing the divisors of a totally decomposable vector is also provided. Several examples are given for which the calculations are too tedious to do by hand and are performed by coding the conditions found into Maple. Our main motivation lies in Lie symmetry, where the invariant subspaces of the adjoint representations for the Lie symmetry algebra of a differential equation must be known explicitly and comprehensively in order to determine all the ideals of the Lie symmetry algebra.</p><h2>Other Information</h2> <p> Published in: Annali di Matematica Pura ed Applicata (1923 -)<br> License: <a href="https://creativecommons.org/licenses/by/4.0" target="_blank">https://creativecommons.org/licenses/by/4.0</a><br>See article on publisher's website: <a href="http://dx.doi.org/10.1007/s10231-022-01233-7" target="_blank">http://dx.doi.org/10.1007/s10231-022-01233-7</a></p>2022-11-22T21:12:46ZTextJournal contributioninfo:eu-repo/semantics/publishedVersiontextcontribution to journal10.1007/s10231-022-01233-7https://figshare.com/articles/journal_contribution/A_novel_procedure_for_constructing_invariant_subspaces_of_a_set_of_matrices/21597156CC BY 4.0info:eu-repo/semantics/openAccessoai:figshare.com:article/215971562022-11-22T21:12:46Z |
| spellingShingle | A novel procedure for constructing invariant subspaces of a set of matrices Ahmad Y. Al-Dweik (14158875) Applied mathematics Applied Mathematics |
| status_str | publishedVersion |
| title | A novel procedure for constructing invariant subspaces of a set of matrices |
| title_full | A novel procedure for constructing invariant subspaces of a set of matrices |
| title_fullStr | A novel procedure for constructing invariant subspaces of a set of matrices |
| title_full_unstemmed | A novel procedure for constructing invariant subspaces of a set of matrices |
| title_short | A novel procedure for constructing invariant subspaces of a set of matrices |
| title_sort | A novel procedure for constructing invariant subspaces of a set of matrices |
| topic | Applied mathematics Applied Mathematics |