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Hermitian completely positive matrices. (English) Zbl 1448.15049
Summary: In this paper, we introduce the Hermitian completely positive (HCP) matrix, which has a Hermitian completely positive (HCP) decomposition with all real and imaginary parts of the decomposition vectors being nonnegative. Some properties of the Hermitian completely positive matrix are given. A semidefinite algorithm is also proposed for checking whether a Hermitian matrix is HCP or not. If a matrix is not HCP, a certificate for it can be obtained; if it is, an HCP decomposition can be obtained.
MSC:
15B57 Hermitian, skew-Hermitian, and related matrices
15A23 Factorization of matrices
44A60 Moment problems
90C22 Semidefinite programming
Software:
GloptiPoly; SeDuMi
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