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Preservers of Completely Positive Matrix Rank for Inclines
A real symmetric matrix A is called completely positive if there exists a nonnegative real n × k matrix B such that A = B B t . The smallest value of k for all possible choices of nonnegative matrices B is called the CP-rank of A . We extend the ideas of complete positivity and the CP-rank to matric...
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| Published in: | Bulletin of the Malaysian Mathematical Sciences Society 2019-03, Vol.42 (2), p.437-447 |
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| Main Authors: | , , |
| Format: | Article |
| Language: | English |
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| cites | cdi_FETCH-LOGICAL-c288t-a9997391c2a716b745e6b2d07b24527bf9897c0b5feeee44a1cf3a31df77a0ee3 |
| container_end_page | 447 |
| container_issue | 2 |
| container_start_page | 437 |
| container_title | Bulletin of the Malaysian Mathematical Sciences Society |
| container_volume | 42 |
| creator | Beasley, LeRoy B. Mohindru, Preeti Pereira, Rajesh |
| description | A real symmetric matrix
A
is called completely positive if there exists a nonnegative real
n
×
k
matrix
B
such that
A
=
B
B
t
. The smallest value of
k
for all possible choices of nonnegative matrices
B
is called the CP-rank of
A
. We extend the ideas of complete positivity and the CP-rank to matrices whose entries are elements of an incline in a similar way. We classify maps on the set of
n
×
n
symmetric matrices over certain inclines which strongly preserve CP-rank-1 matrices as well as maps which preserve CP-rank-1 and CP-rank-
k
. The result suggests that there is a certain standard class of solutions for CP-rank preserver problems on incline matrices. |
| doi_str_mv | 10.1007/s40840-017-0490-z |
| format | article |
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A
is called completely positive if there exists a nonnegative real
n
×
k
matrix
B
such that
A
=
B
B
t
. The smallest value of
k
for all possible choices of nonnegative matrices
B
is called the CP-rank of
A
. We extend the ideas of complete positivity and the CP-rank to matrices whose entries are elements of an incline in a similar way. We classify maps on the set of
n
×
n
symmetric matrices over certain inclines which strongly preserve CP-rank-1 matrices as well as maps which preserve CP-rank-1 and CP-rank-
k
. The result suggests that there is a certain standard class of solutions for CP-rank preserver problems on incline matrices.</description><identifier>ISSN: 0126-6705</identifier><identifier>EISSN: 2180-4206</identifier><identifier>DOI: 10.1007/s40840-017-0490-z</identifier><language>eng</language><publisher>Singapore: Springer Singapore</publisher><subject>Applications of Mathematics ; Mathematics ; Mathematics and Statistics</subject><ispartof>Bulletin of the Malaysian Mathematical Sciences Society, 2019-03, Vol.42 (2), p.437-447</ispartof><rights>Malaysian Mathematical Sciences Society and Penerbit Universiti Sains Malaysia 2017</rights><lds50>peer_reviewed</lds50><woscitedreferencessubscribed>false</woscitedreferencessubscribed><citedby>FETCH-LOGICAL-c288t-a9997391c2a716b745e6b2d07b24527bf9897c0b5feeee44a1cf3a31df77a0ee3</citedby><cites>FETCH-LOGICAL-c288t-a9997391c2a716b745e6b2d07b24527bf9897c0b5feeee44a1cf3a31df77a0ee3</cites></display><links><openurl>$$Topenurl_article</openurl><openurlfulltext>$$Topenurlfull_article</openurlfulltext><thumbnail>$$Tsyndetics_thumb_exl</thumbnail><link.rule.ids>314,780,784,27924,27925</link.rule.ids></links><search><creatorcontrib>Beasley, LeRoy B.</creatorcontrib><creatorcontrib>Mohindru, Preeti</creatorcontrib><creatorcontrib>Pereira, Rajesh</creatorcontrib><title>Preservers of Completely Positive Matrix Rank for Inclines</title><title>Bulletin of the Malaysian Mathematical Sciences Society</title><addtitle>Bull. Malays. Math. Sci. Soc</addtitle><description>A real symmetric matrix
A
is called completely positive if there exists a nonnegative real
n
×
k
matrix
B
such that
A
=
B
B
t
. The smallest value of
k
for all possible choices of nonnegative matrices
B
is called the CP-rank of
A
. We extend the ideas of complete positivity and the CP-rank to matrices whose entries are elements of an incline in a similar way. We classify maps on the set of
n
×
n
symmetric matrices over certain inclines which strongly preserve CP-rank-1 matrices as well as maps which preserve CP-rank-1 and CP-rank-
k
. The result suggests that there is a certain standard class of solutions for CP-rank preserver problems on incline matrices.</description><subject>Applications of Mathematics</subject><subject>Mathematics</subject><subject>Mathematics and Statistics</subject><issn>0126-6705</issn><issn>2180-4206</issn><fulltext>true</fulltext><rsrctype>article</rsrctype><creationdate>2019</creationdate><recordtype>article</recordtype><recordid>eNp9j8tOwzAQRS0EElHpB7DzDxjGjmPH7FDEo1IRFYK15aRjlJLGlR0q2q8nVVhzN7O5Z3QPIdccbjiAvk0SSgkMuGYgDbDjGckEL4FJAeqcZMCFYkpDcUnmKW1gTKGEEjwjd6uICeMeY6LB0ypsdx0O2B3oKqR2aPdIX9wQ2x_65vov6kOki77p2h7TFbnwrks4_7sz8vH48F49s-Xr06K6X7JGlOXAnDFG54Y3wmmuai0LVLVYg66FLISuvSmNbqAuPI6R0vHG5y7na6-1A8R8Rvj0t4khpYje7mK7dfFgOdiTv5387ehvT_72ODJiYtLY7T8x2k34jv048x_oFxW1Xik</recordid><startdate>20190315</startdate><enddate>20190315</enddate><creator>Beasley, LeRoy B.</creator><creator>Mohindru, Preeti</creator><creator>Pereira, Rajesh</creator><general>Springer Singapore</general><scope>AAYXX</scope><scope>CITATION</scope></search><sort><creationdate>20190315</creationdate><title>Preservers of Completely Positive Matrix Rank for Inclines</title><author>Beasley, LeRoy B. ; Mohindru, Preeti ; Pereira, Rajesh</author></sort><facets><frbrtype>5</frbrtype><frbrgroupid>cdi_FETCH-LOGICAL-c288t-a9997391c2a716b745e6b2d07b24527bf9897c0b5feeee44a1cf3a31df77a0ee3</frbrgroupid><rsrctype>articles</rsrctype><prefilter>articles</prefilter><language>eng</language><creationdate>2019</creationdate><topic>Applications of Mathematics</topic><topic>Mathematics</topic><topic>Mathematics and Statistics</topic><toplevel>peer_reviewed</toplevel><toplevel>online_resources</toplevel><creatorcontrib>Beasley, LeRoy B.</creatorcontrib><creatorcontrib>Mohindru, Preeti</creatorcontrib><creatorcontrib>Pereira, Rajesh</creatorcontrib><collection>CrossRef</collection><jtitle>Bulletin of the Malaysian Mathematical Sciences Society</jtitle></facets><delivery><delcategory>Remote Search Resource</delcategory><fulltext>fulltext</fulltext></delivery><addata><au>Beasley, LeRoy B.</au><au>Mohindru, Preeti</au><au>Pereira, Rajesh</au><format>journal</format><genre>article</genre><ristype>JOUR</ristype><atitle>Preservers of Completely Positive Matrix Rank for Inclines</atitle><jtitle>Bulletin of the Malaysian Mathematical Sciences Society</jtitle><stitle>Bull. Malays. Math. Sci. Soc</stitle><date>2019-03-15</date><risdate>2019</risdate><volume>42</volume><issue>2</issue><spage>437</spage><epage>447</epage><pages>437-447</pages><issn>0126-6705</issn><eissn>2180-4206</eissn><abstract>A real symmetric matrix
A
is called completely positive if there exists a nonnegative real
n
×
k
matrix
B
such that
A
=
B
B
t
. The smallest value of
k
for all possible choices of nonnegative matrices
B
is called the CP-rank of
A
. We extend the ideas of complete positivity and the CP-rank to matrices whose entries are elements of an incline in a similar way. We classify maps on the set of
n
×
n
symmetric matrices over certain inclines which strongly preserve CP-rank-1 matrices as well as maps which preserve CP-rank-1 and CP-rank-
k
. The result suggests that there is a certain standard class of solutions for CP-rank preserver problems on incline matrices.</abstract><cop>Singapore</cop><pub>Springer Singapore</pub><doi>10.1007/s40840-017-0490-z</doi><tpages>11</tpages></addata></record> |
| fulltext | fulltext |
| identifier | ISSN: 0126-6705 |
| ispartof | Bulletin of the Malaysian Mathematical Sciences Society, 2019-03, Vol.42 (2), p.437-447 |
| issn | 0126-6705 2180-4206 |
| language | eng |
| recordid | cdi_crossref_primary_10_1007_s40840_017_0490_z |
| source | Springer Nature |
| subjects | Applications of Mathematics Mathematics Mathematics and Statistics |
| title | Preservers of Completely Positive Matrix Rank for Inclines |
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