Matrices With High Completely Positive Semidefinite Rank

@article{Gribling2017MatricesWH,
  title={Matrices With High Completely Positive Semidefinite Rank},
  author={S. Gribling and David de Laat and M. Laurent},
  journal={Linear Algebra and its Applications},
  year={2017},
  volume={513},
  pages={122-148}
}
  • S. Gribling, David de Laat, M. Laurent
  • Published 2017
  • Mathematics
  • Linear Algebra and its Applications
  • A real symmetric matrix M is completely positive semidefinite if it admits a Gram representation by (Hermitian) positive semidefinite matrices of any size d. The smallest such d is called the (complex) completely positive semidefinite rank of M, and it is an open question whether there exists an upper bound on this number as a function of the matrix size. We construct completely positive semidefinite matrices of size 4k2+2k+2 with complex completely positive semidefinite rank 2k for any… CONTINUE READING
    Correlation matrices, Clifford algebras, and completely positive semidefinite rank
    • 2
    • Highly Influenced
    • PDF
    Algorithms for positive semidefinite factorization
    • 3
    • PDF
    Completely positive semidefinite rank
    • 6
    • PDF
    Universal Rigidity of Complete Bipartite Graphs
    • 10
    • PDF
    Introduction to Nonnegative Matrix Factorization
    • 28
    • PDF

    References

    Publications referenced by this paper.
    SHOWING 1-10 OF 46 REFERENCES
    On the Closure of the Completely Positive Semidefinite Cone and Linear Approximations to Quantum Colorings
    • 10
    • PDF
    A Note on Extreme Correlation Matrices
    • 63
    Positive semidefinite matrix completion, universal rigidity and the Strong Arnold Property
    • 26
    • PDF
    Positive semidefinite rank
    • 63
    • PDF
    Lifts of Convex Sets and Cone Factorizations
    • 141
    • PDF
    Approximation of the Stability Number of a Graph via Copositive Programming
    • 285
    • PDF