The Effect of the Additive Row Operation on the Permanent
The permanent function is not as stable as the determinant function under the elementary row operations. For example, adding a non-zero scalar multiple of a row to another row does not change the determinant of a matrix, but this operation changes its permanent. In this article, the variation in the...
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| Format: | Article |
| Language: | English |
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Naim Çağman
2023-03-01
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| Series: | Journal of New Theory |
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| Online Access: | https://dergipark.org.tr/en/download/article-file/2666140 |
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| author | Abdullah Talha Sözer Ahmet Zahid Küçük |
| author_facet | Abdullah Talha Sözer Ahmet Zahid Küçük |
| author_sort | Abdullah Talha Sözer |
| collection | DOAJ |
| description | The permanent function is not as stable as the determinant function under the elementary row operations. For example, adding a non-zero scalar multiple of a row to another row does not change the determinant of a matrix, but this operation changes its permanent. In this article, the variation in the permanent by applying the operation, which adds a scalar multiple of a row to another row, is examined. The relationship between the permanent of the matrix to which this operation is applied and the permanent of the initial matrix is given by a theorem. Finally, the paper inquires the need for further research. |
| format | Article |
| id | doaj-art-9f911b1fda61444e8df5609865ff047d |
| institution | DOAJ |
| issn | 2149-1402 |
| language | English |
| publishDate | 2023-03-01 |
| publisher | Naim Çağman |
| record_format | Article |
| series | Journal of New Theory |
| spelling | doaj-art-9f911b1fda61444e8df5609865ff047d2025-08-20T03:10:57ZengNaim ÇağmanJournal of New Theory2149-14022023-03-014281310.53570/jnt.11789902425The Effect of the Additive Row Operation on the PermanentAbdullah Talha Sözer0https://orcid.org/0000-0002-7855-6119Ahmet Zahid Küçük1https://orcid.org/0000-0001-6816-6478KARABÜK ÜNİVERSİTESİKarabük ÜniversitesiThe permanent function is not as stable as the determinant function under the elementary row operations. For example, adding a non-zero scalar multiple of a row to another row does not change the determinant of a matrix, but this operation changes its permanent. In this article, the variation in the permanent by applying the operation, which adds a scalar multiple of a row to another row, is examined. The relationship between the permanent of the matrix to which this operation is applied and the permanent of the initial matrix is given by a theorem. Finally, the paper inquires the need for further research.https://dergipark.org.tr/en/download/article-file/2666140permanentgaussian eliminationelementary row operationslaplace expansion |
| spellingShingle | Abdullah Talha Sözer Ahmet Zahid Küçük The Effect of the Additive Row Operation on the Permanent Journal of New Theory permanent gaussian elimination elementary row operations laplace expansion |
| title | The Effect of the Additive Row Operation on the Permanent |
| title_full | The Effect of the Additive Row Operation on the Permanent |
| title_fullStr | The Effect of the Additive Row Operation on the Permanent |
| title_full_unstemmed | The Effect of the Additive Row Operation on the Permanent |
| title_short | The Effect of the Additive Row Operation on the Permanent |
| title_sort | effect of the additive row operation on the permanent |
| topic | permanent gaussian elimination elementary row operations laplace expansion |
| url | https://dergipark.org.tr/en/download/article-file/2666140 |
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