Completely positive matrices over Boolean algebras and their CP-rank
Drew, Johnson and Loewy conjectured that for n ≥ 4, the CP-rank of every n × n completely positive real matrix is at most [n2/4]. In this paper, we prove this conjecture for n × n completely positive matrices over Boolean algebras (finite or infinite). In addition,we formulate various CP-rank inequa...
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De Gruyter
2015-04-01
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| Series: | Special Matrices |
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| Online Access: | http://www.degruyter.com/view/j/spma.2015.3.issue-1/spma-2015-0007/spma-2015-0007.xml?format=INT |
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doaj-596cca98707e40fda2e0a210db22858c2021-10-02T09:50:28ZengDe GruyterSpecial Matrices2300-74512015-04-013110.1515/spma-2015-0007spma-2015-0007Completely positive matrices over Boolean algebras and their CP-rankMohindru Preeti0Department of Mathematics Drew, Johnson and Loewy conjectured that for n ≥ 4, the CP-rank of every n × n completely positive real matrix is at most [n2/4]. In this paper, we prove this conjecture for n × n completely positive matrices over Boolean algebras (finite or infinite). In addition,we formulate various CP-rank inequalities of completely positive matrices over special semirings using semiring homomorphisms.http://www.degruyter.com/view/j/spma.2015.3.issue-1/spma-2015-0007/spma-2015-0007.xml?format=INTBoolean matrices matrices over semirings completely positive matrices diagonally dominant matrices semiring homomorphisms15B33 15B34 15B48 16A78 |
| collection |
DOAJ |
| language |
English |
| format |
Article |
| sources |
DOAJ |
| author |
Mohindru Preeti |
| spellingShingle |
Mohindru Preeti Completely positive matrices over Boolean algebras and their CP-rank Special Matrices Boolean matrices matrices over semirings completely positive matrices diagonally dominant matrices semiring homomorphisms 15B33 15B34 15B48 16A78 |
| author_facet |
Mohindru Preeti |
| author_sort |
Mohindru Preeti |
| title |
Completely positive matrices over Boolean algebras and their CP-rank |
| title_short |
Completely positive matrices over Boolean algebras and their CP-rank |
| title_full |
Completely positive matrices over Boolean algebras and their CP-rank |
| title_fullStr |
Completely positive matrices over Boolean algebras and their CP-rank |
| title_full_unstemmed |
Completely positive matrices over Boolean algebras and their CP-rank |
| title_sort |
completely positive matrices over boolean algebras and their cp-rank |
| publisher |
De Gruyter |
| series |
Special Matrices |
| issn |
2300-7451 |
| publishDate |
2015-04-01 |
| description |
Drew, Johnson and Loewy conjectured that for n ≥ 4, the CP-rank of every n × n completely positive real matrix is at most [n2/4]. In this paper, we prove this conjecture for n × n completely positive matrices over Boolean algebras (finite or infinite). In addition,we formulate various CP-rank inequalities of completely positive matrices over special semirings using semiring homomorphisms. |
| topic |
Boolean matrices matrices over semirings completely positive matrices diagonally dominant matrices semiring homomorphisms 15B33 15B34 15B48 16A78 |
| url |
http://www.degruyter.com/view/j/spma.2015.3.issue-1/spma-2015-0007/spma-2015-0007.xml?format=INT |
| work_keys_str_mv |
AT mohindrupreeti completelypositivematricesoverbooleanalgebrasandtheircprank |
| _version_ |
1716856533293203456 |