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Completely Positive Matrices: Real, Rational, and Integral
Abraham Berman
,
Naomi Shaked-Monderer
Abstract
This paper was presented as an invited talk in the 6th International Conference on Matrix Analysis and Applications, Duy Tan University, Da Nang City, Vietnam, June 15–18, 2017. All the matrices in the paper are real. We survey known results and present some new problems. The paper has six parts.
1. What is complete positivity?
2. Why are completely positive matrices important?
3. How can we tell if a given matrix is completely positive?
4. Does every rational completely positive matrix have a rational cp-factorization?
5. cp-rank.
6. Which integral completely positive matrices have an integral cp-factorization?