Linear transformations of tropical matrices preserving the cyclicity index
We combine matrix theory and graph theory methods to give a complete characterization of the surjective linear transformations of tropical matrices that preserve the cyclicity index. We show that there are non-surjective linear transformations that preserve the cyclicity index and we leave it open t...
| Main Authors: | , , |
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| Format: | Article |
| Language: | English |
| Published: |
De Gruyter
2021-03-01
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| Series: | Special Matrices |
| Subjects: | |
| Online Access: | https://doi.org/10.1515/spma-2020-0128 |
| _version_ | 1818355949979566080 |
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| author | Guterman Alexander Kreines Elena Thomassen Carsten |
| author_facet | Guterman Alexander Kreines Elena Thomassen Carsten |
| author_sort | Guterman Alexander |
| collection | DOAJ |
| description | We combine matrix theory and graph theory methods to give a complete characterization of the surjective linear transformations of tropical matrices that preserve the cyclicity index. We show that there are non-surjective linear transformations that preserve the cyclicity index and we leave it open to characterize those. |
| first_indexed | 2024-12-13T19:49:27Z |
| format | Article |
| id | doaj.art-4faac12c18c94cf8b8af6297d04df621 |
| institution | Directory Open Access Journal |
| issn | 2300-7451 |
| language | English |
| last_indexed | 2024-12-13T19:49:27Z |
| publishDate | 2021-03-01 |
| publisher | De Gruyter |
| record_format | Article |
| series | Special Matrices |
| spelling | doaj.art-4faac12c18c94cf8b8af6297d04df6212022-12-21T23:33:28ZengDe GruyterSpecial Matrices2300-74512021-03-019111211810.1515/spma-2020-0128Linear transformations of tropical matrices preserving the cyclicity indexGuterman Alexander0Kreines Elena1Thomassen Carsten2Faculty of Mathematics and Mechanics, Moscow State University, Moscow, GSP-1, 119991, Russia; Moscow Center for Fundamental and Applied Mathematics, Moscow, GSP-1, 119991, Russia; Moscow Institute of Physics and Technology, Dolgoprudny, 141701, RussiaFaculty of Mathematics and Mechanics, Moscow State University, Moscow, GSP-1, 119991, Russia; Moscow Center for Fundamental and Applied Mathematics, Moscow, GSP-1, 119991, RussiaDepartment of Applied Mathematics and Computer Science, Technical University of Denmark, DK-2800Lyngby, DenmarkWe combine matrix theory and graph theory methods to give a complete characterization of the surjective linear transformations of tropical matrices that preserve the cyclicity index. We show that there are non-surjective linear transformations that preserve the cyclicity index and we leave it open to characterize those.https://doi.org/10.1515/spma-2020-0128tropical linear algebracyclicity indexlinear preservers |
| spellingShingle | Guterman Alexander Kreines Elena Thomassen Carsten Linear transformations of tropical matrices preserving the cyclicity index Special Matrices tropical linear algebra cyclicity index linear preservers |
| title | Linear transformations of tropical matrices preserving the cyclicity index |
| title_full | Linear transformations of tropical matrices preserving the cyclicity index |
| title_fullStr | Linear transformations of tropical matrices preserving the cyclicity index |
| title_full_unstemmed | Linear transformations of tropical matrices preserving the cyclicity index |
| title_short | Linear transformations of tropical matrices preserving the cyclicity index |
| title_sort | linear transformations of tropical matrices preserving the cyclicity index |
| topic | tropical linear algebra cyclicity index linear preservers |
| url | https://doi.org/10.1515/spma-2020-0128 |
| work_keys_str_mv | AT gutermanalexander lineartransformationsoftropicalmatricespreservingthecyclicityindex AT kreineselena lineartransformationsoftropicalmatricespreservingthecyclicityindex AT thomassencarsten lineartransformationsoftropicalmatricespreservingthecyclicityindex |