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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Bibliographic Details
Published in:Bulletin of the Malaysian Mathematical Sciences Society 2019-03, Vol.42 (2), p.437-447
Main Authors: Beasley, LeRoy B., Mohindru, Preeti, Pereira, Rajesh
Format: Article
Language:English
Subjects:
Applications of Mathematics
Mathematics
Mathematics and Statistics
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Summary: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.
ISSN:0126-6705
2180-4206
DOI:10.1007/s40840-017-0490-z