Ranks of permutative matrices
A new type of matrix, termed permutative, is defined and motivated herein. The focus is upon identifying circumstances under which square permutative matrices are rank deficient. Two distinct ways, along with variants upon them are given. These are a special kind of grouping of rows and a type of pa...
| Main Authors: | , , , |
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| Format: | Article |
| Language: | English |
| Published: |
De Gruyter
2016-06-01
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| Series: | Special Matrices |
| Subjects: | |
| Online Access: | http://www.degruyter.com/view/j/spma.2016.4.issue-1/spma-2016-0022/spma-2016-0022.xml?format=INT |
| _version_ | 1818587640298995712 |
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| author | Hu Xiaonan Johnson Charles R. Davis Caroline E. Zhang Yimeng |
| author_facet | Hu Xiaonan Johnson Charles R. Davis Caroline E. Zhang Yimeng |
| author_sort | Hu Xiaonan |
| collection | DOAJ |
| description | A new type of matrix, termed permutative, is defined and motivated herein. The focus is upon identifying
circumstances under which square permutative matrices are rank deficient. Two distinct ways, along
with variants upon them are given. These are a special kind of grouping of rows and a type of partition in
which the blocks are again permutative. Other, results are given, along with some questions and conjectures. |
| first_indexed | 2024-12-16T09:12:04Z |
| format | Article |
| id | doaj.art-b4d0bc72ee1f491080e7a94741858af0 |
| institution | Directory Open Access Journal |
| issn | 2300-7451 |
| language | English |
| last_indexed | 2024-12-16T09:12:04Z |
| publishDate | 2016-06-01 |
| publisher | De Gruyter |
| record_format | Article |
| series | Special Matrices |
| spelling | doaj.art-b4d0bc72ee1f491080e7a94741858af02022-12-21T22:36:58ZengDe GruyterSpecial Matrices2300-74512016-06-014110.1515/spma-2016-0022spma-2016-0022Ranks of permutative matricesHu Xiaonan0Johnson Charles R.1Davis Caroline E.2Zhang Yimeng3Department of Mathematics, College of William and Mary, P.O.Box 8795, Williamsburg, VA 23187Department of Mathematics, College of William and Mary, P.O.Box 8795, Williamsburg, VA 23187Department of Mathematics, College of William and Mary, P.O.Box 8795, Williamsburg, VA 23187Department of Mathematics, College of William and Mary, P.O.Box 8795, Williamsburg, VA 23187A new type of matrix, termed permutative, is defined and motivated herein. The focus is upon identifying circumstances under which square permutative matrices are rank deficient. Two distinct ways, along with variants upon them are given. These are a special kind of grouping of rows and a type of partition in which the blocks are again permutative. Other, results are given, along with some questions and conjectures.http://www.degruyter.com/view/j/spma.2016.4.issue-1/spma-2016-0022/spma-2016-0022.xml?format=INTh, k-partition h, k, g-partition Identically singular Latin square Permutative matrix Polynomial matrix Row grouping |
| spellingShingle | Hu Xiaonan Johnson Charles R. Davis Caroline E. Zhang Yimeng Ranks of permutative matrices Special Matrices h, k-partition h, k, g-partition Identically singular Latin square Permutative matrix Polynomial matrix Row grouping |
| title | Ranks of permutative matrices |
| title_full | Ranks of permutative matrices |
| title_fullStr | Ranks of permutative matrices |
| title_full_unstemmed | Ranks of permutative matrices |
| title_short | Ranks of permutative matrices |
| title_sort | ranks of permutative matrices |
| topic | h, k-partition h, k, g-partition Identically singular Latin square Permutative matrix Polynomial matrix Row grouping |
| url | http://www.degruyter.com/view/j/spma.2016.4.issue-1/spma-2016-0022/spma-2016-0022.xml?format=INT |
| work_keys_str_mv | AT huxiaonan ranksofpermutativematrices AT johnsoncharlesr ranksofpermutativematrices AT daviscarolinee ranksofpermutativematrices AT zhangyimeng ranksofpermutativematrices |