The Tropical Matrix Groups with Symmetric Idempotents
In this paper we study the semigroup Mn(T) of all n×n tropical matrices under multiplication. We give a description of the tropical matrix groups containing a diagonal block idempotent matrix in which the main diagonal blocks are real matrices and other blocks are zero matrices. We show that each no...
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| Format: | Article |
| Language: | English |
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Wiley
2018-01-01
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| Series: | Discrete Dynamics in Nature and Society |
| Online Access: | http://dx.doi.org/10.1155/2018/4797638 |
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| author | Lin Yang |
| author_facet | Lin Yang |
| author_sort | Lin Yang |
| collection | DOAJ |
| description | In this paper we study the semigroup Mn(T) of all n×n tropical matrices under multiplication. We give a description of the tropical matrix groups containing a diagonal block idempotent matrix in which the main diagonal blocks are real matrices and other blocks are zero matrices. We show that each nonsingular symmetric idempotent matrix is equivalent to this type of block diagonal matrix. Based upon this result, we give some decompositions of the maximal subgroups of Mn(T) which contain symmetric idempotents. |
| format | Article |
| id | doaj-art-ce300ab9a5714ddebf61312aa371bfd7 |
| institution | DOAJ |
| issn | 1026-0226 1607-887X |
| language | English |
| publishDate | 2018-01-01 |
| publisher | Wiley |
| record_format | Article |
| series | Discrete Dynamics in Nature and Society |
| spelling | doaj-art-ce300ab9a5714ddebf61312aa371bfd72025-08-20T03:19:41ZengWileyDiscrete Dynamics in Nature and Society1026-02261607-887X2018-01-01201810.1155/2018/47976384797638The Tropical Matrix Groups with Symmetric IdempotentsLin Yang0School of Science, Lanzhou University of Technology, Lanzhou, Gansu 730050, ChinaIn this paper we study the semigroup Mn(T) of all n×n tropical matrices under multiplication. We give a description of the tropical matrix groups containing a diagonal block idempotent matrix in which the main diagonal blocks are real matrices and other blocks are zero matrices. We show that each nonsingular symmetric idempotent matrix is equivalent to this type of block diagonal matrix. Based upon this result, we give some decompositions of the maximal subgroups of Mn(T) which contain symmetric idempotents.http://dx.doi.org/10.1155/2018/4797638 |
| spellingShingle | Lin Yang The Tropical Matrix Groups with Symmetric Idempotents Discrete Dynamics in Nature and Society |
| title | The Tropical Matrix Groups with Symmetric Idempotents |
| title_full | The Tropical Matrix Groups with Symmetric Idempotents |
| title_fullStr | The Tropical Matrix Groups with Symmetric Idempotents |
| title_full_unstemmed | The Tropical Matrix Groups with Symmetric Idempotents |
| title_short | The Tropical Matrix Groups with Symmetric Idempotents |
| title_sort | tropical matrix groups with symmetric idempotents |
| url | http://dx.doi.org/10.1155/2018/4797638 |
| work_keys_str_mv | AT linyang thetropicalmatrixgroupswithsymmetricidempotents AT linyang tropicalmatrixgroupswithsymmetricidempotents |