Matrices With High Completely Positive Semidefinite Rank

  title={Matrices With High Completely Positive Semidefinite Rank},
  author={S. Gribling and David de Laat and M. Laurent},
  journal={Linear Algebra and its Applications},
  • 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
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