ORTHOGONAL REPRESENTATION OF THE PROPER TRANSFORMATION OF A PERSYMMETRIC MATRIX BASED ON ROTATION OPERATORS
The mathematical substantiation of the algorithm for synthesis of the proper transformation and finding the eigenvalue formulae of a persymmetric matrix of dimension N = 2 k ( k =1, 4 ) based on orthogonal rotation operators is given. The proposed algorithm made it possible to improve the author...
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| Format: | Article |
| Language: | Russian |
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National Academy of Sciences of Belarus, the United Institute of Informatics Problems
2018-03-01
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| Series: | Informatika |
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| Online Access: | https://inf.grid.by/jour/article/view/314 |
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| _version_ | 1832543202820751360 |
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| author | V. M. Demko |
| author_facet | V. M. Demko |
| author_sort | V. M. Demko |
| collection | DOAJ |
| description | The mathematical substantiation of the algorithm for synthesis of the proper transformation and finding the eigenvalue formulae of a persymmetric matrix of dimension N = 2 k ( k =1, 4 ) based on orthogonal rotation operators is given. The proposed algorithm made it possible to improve the author's approach to calculating eigenvalues based on numerical examples for the maximal dimension of matrices 64×64, resulting the possibility to obtain analytical relations for calculating the eigenvalues of the persymmetric matrix. It is shown that the proper transformation has a factorized structure in the form of a product of rotation operators, each of which is a direct sum of elementary Givens and Jacobian rotation matrices. |
| format | Article |
| id | doaj-art-18157fe7b61e4dcab1721d30579dd127 |
| institution | Kabale University |
| issn | 1816-0301 |
| language | Russian |
| publishDate | 2018-03-01 |
| publisher | National Academy of Sciences of Belarus, the United Institute of Informatics Problems |
| record_format | Article |
| series | Informatika |
| spelling | doaj-art-18157fe7b61e4dcab1721d30579dd1272025-02-03T11:51:43ZrusNational Academy of Sciences of Belarus, the United Institute of Informatics ProblemsInformatika1816-03012018-03-011513450296ORTHOGONAL REPRESENTATION OF THE PROPER TRANSFORMATION OF A PERSYMMETRIC MATRIX BASED ON ROTATION OPERATORSV. M. Demko0United Institute of Informatics Problems of the National Academy of Sciences of BelarusThe mathematical substantiation of the algorithm for synthesis of the proper transformation and finding the eigenvalue formulae of a persymmetric matrix of dimension N = 2 k ( k =1, 4 ) based on orthogonal rotation operators is given. The proposed algorithm made it possible to improve the author's approach to calculating eigenvalues based on numerical examples for the maximal dimension of matrices 64×64, resulting the possibility to obtain analytical relations for calculating the eigenvalues of the persymmetric matrix. It is shown that the proper transformation has a factorized structure in the form of a product of rotation operators, each of which is a direct sum of elementary Givens and Jacobian rotation matrices.https://inf.grid.by/jour/article/view/314persymmetric matrixeigenvaluesrotation operators |
| spellingShingle | V. M. Demko ORTHOGONAL REPRESENTATION OF THE PROPER TRANSFORMATION OF A PERSYMMETRIC MATRIX BASED ON ROTATION OPERATORS Informatika persymmetric matrix eigenvalues rotation operators |
| title | ORTHOGONAL REPRESENTATION OF THE PROPER TRANSFORMATION OF A PERSYMMETRIC MATRIX BASED ON ROTATION OPERATORS |
| title_full | ORTHOGONAL REPRESENTATION OF THE PROPER TRANSFORMATION OF A PERSYMMETRIC MATRIX BASED ON ROTATION OPERATORS |
| title_fullStr | ORTHOGONAL REPRESENTATION OF THE PROPER TRANSFORMATION OF A PERSYMMETRIC MATRIX BASED ON ROTATION OPERATORS |
| title_full_unstemmed | ORTHOGONAL REPRESENTATION OF THE PROPER TRANSFORMATION OF A PERSYMMETRIC MATRIX BASED ON ROTATION OPERATORS |
| title_short | ORTHOGONAL REPRESENTATION OF THE PROPER TRANSFORMATION OF A PERSYMMETRIC MATRIX BASED ON ROTATION OPERATORS |
| title_sort | orthogonal representation of the proper transformation of a persymmetric matrix based on rotation operators |
| topic | persymmetric matrix eigenvalues rotation operators |
| url | https://inf.grid.by/jour/article/view/314 |
| work_keys_str_mv | AT vmdemko orthogonalrepresentationofthepropertransformationofapersymmetricmatrixbasedonrotationoperators |