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Completely Positive Matrices: Real, Rational, and Integral

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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. 1.

    What is complete positivity?

  2. 2.

    Why are completely positive matrices important?

  3. 3.

    How can we tell if a given matrix is completely positive?

  4. 4.

    Does every rational completely positive matrix have a rational cp-factorization?

  5. 5.

    cp-rank.

  6. 6.

    Which integral completely positive matrices have an integral cp-factorization?

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Funding

This work was supported by grant no. 2219/15 by the ISF-NSFC joint scientific research program.

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Authors and Affiliations

  1. Department of Mathematics, Technion-Israel Institute of Technology, Haifa, 32000, Israel

    Abraham Berman

  2. The Max Stern Yezreel Valley College, Yezreel Valley, 1930600, Israel

    Naomi Shaked-Monderer

Authors
  1. Abraham Berman
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  2. Naomi Shaked-Monderer
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Correspondence to Abraham Berman.

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Berman, A., Shaked-Monderer, N. Completely Positive Matrices: Real, Rational, and Integral. Acta Math Vietnam 43, 629–639 (2018). https://doi.org/10.1007/s40306-018-0254-3

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  • DOI: https://doi.org/10.1007/s40306-018-0254-3

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