New approach to finding eigenvectors for repeated eigenvalues of a matrix
An efficient method of calculating eigenvectors for multiple eigenvalues of a matrix is proposed. This method is based on a formalized transformation of the problem of solving degenerate systems of equations into a regular problem by “repairing” their matrices and correspondingly correcting the righ...
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| Format: | Article |
| Language: | Ukrainian |
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Igor Sikorsky Kyiv Polytechnic Institute
2024-12-01
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| Series: | Sistemnì Doslìdženâ ta Informacìjnì Tehnologìï |
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| Online Access: | http://journal.iasa.kpi.ua/article/view/322526 |
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| _version_ | 1850145216352223232 |
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| author | Anatolii Petrenko |
| author_facet | Anatolii Petrenko |
| author_sort | Anatolii Petrenko |
| collection | DOAJ |
| description | An efficient method of calculating eigenvectors for multiple eigenvalues of a matrix is proposed. This method is based on a formalized transformation of the problem of solving degenerate systems of equations into a regular problem by “repairing” their matrices and correspondingly correcting the right-hand sides of the equations, as well as “exclusion” during calculations from the spectrum eigenvalues of the matrix of one of the multiple values. In the case of non-defective multiples of the matrix, orthogonal eigenvectors are formed in contrast to the results obtained using the Mathematica program. |
| format | Article |
| id | doaj-art-afafb0ebbf9d4dfebbfd091d7c6df85d |
| institution | OA Journals |
| issn | 1681-6048 2308-8893 |
| language | Ukrainian |
| publishDate | 2024-12-01 |
| publisher | Igor Sikorsky Kyiv Polytechnic Institute |
| record_format | Article |
| series | Sistemnì Doslìdženâ ta Informacìjnì Tehnologìï |
| spelling | doaj-art-afafb0ebbf9d4dfebbfd091d7c6df85d2025-08-20T02:28:08ZukrIgor Sikorsky Kyiv Polytechnic InstituteSistemnì Doslìdženâ ta Informacìjnì Tehnologìï1681-60482308-88932024-12-01410711610.20535/SRIT.2308-8893.2024.4.09361241New approach to finding eigenvectors for repeated eigenvalues of a matrixAnatolii Petrenko0https://orcid.org/0000-0001-6712-7792Educational and Research Institute for Applied System Analysis of the National Technical University of Ukraine "Igor Sikorsky Kyiv Polytechnic Institute", KyivAn efficient method of calculating eigenvectors for multiple eigenvalues of a matrix is proposed. This method is based on a formalized transformation of the problem of solving degenerate systems of equations into a regular problem by “repairing” their matrices and correspondingly correcting the right-hand sides of the equations, as well as “exclusion” during calculations from the spectrum eigenvalues of the matrix of one of the multiple values. In the case of non-defective multiples of the matrix, orthogonal eigenvectors are formed in contrast to the results obtained using the Mathematica program.http://journal.iasa.kpi.ua/article/view/322526eigenvectorsmultiples of eigenvaluesalgebraic and geometric multiplicitysolutions of degenerate systemschange of spectrum of a matrixdefective and non-defective multiples of a matrix |
| spellingShingle | Anatolii Petrenko New approach to finding eigenvectors for repeated eigenvalues of a matrix Sistemnì Doslìdženâ ta Informacìjnì Tehnologìï eigenvectors multiples of eigenvalues algebraic and geometric multiplicity solutions of degenerate systems change of spectrum of a matrix defective and non-defective multiples of a matrix |
| title | New approach to finding eigenvectors for repeated eigenvalues of a matrix |
| title_full | New approach to finding eigenvectors for repeated eigenvalues of a matrix |
| title_fullStr | New approach to finding eigenvectors for repeated eigenvalues of a matrix |
| title_full_unstemmed | New approach to finding eigenvectors for repeated eigenvalues of a matrix |
| title_short | New approach to finding eigenvectors for repeated eigenvalues of a matrix |
| title_sort | new approach to finding eigenvectors for repeated eigenvalues of a matrix |
| topic | eigenvectors multiples of eigenvalues algebraic and geometric multiplicity solutions of degenerate systems change of spectrum of a matrix defective and non-defective multiples of a matrix |
| url | http://journal.iasa.kpi.ua/article/view/322526 |
| work_keys_str_mv | AT anatoliipetrenko newapproachtofindingeigenvectorsforrepeatedeigenvaluesofamatrix |