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Preservers of Completely Positive Matrix Rank for Inclines

  • LeRoy B. BeasleyEmail author
  • Preeti Mohindru
  • Rajesh Pereira
Article
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Abstract

A real symmetric matrix A is called completely positive if there exists a nonnegative real \(n\times k\) matrix B such that \(A = BB^{t}\). 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 \(n \times n\) 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.

Keywords

Semirings Inclines Completely positive matrices Cp-rank (Strong) linear preservers 

Mathematics Subject Classification

15A86 

Notes

Acknowledgements

The authors would like to thank the referees for their careful reading of the paper and for many helpful suggestions which greatly improved the paper.

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Copyright information

© Malaysian Mathematical Sciences Society and Penerbit Universiti Sains Malaysia 2017

Authors and Affiliations

  • LeRoy B. Beasley
    • 1
    Email author
  • Preeti Mohindru
    • 2
  • Rajesh Pereira
    • 3
  1. 1.Department of Mathematics and StatisticsUtah State UniversityLoganUSA
  2. 2.Cogswell CollegeSan JoseUSA
  3. 3.Department of Mathematics and StatisticsUniversity of GuelphGuelphCanada

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