On the completely positive and positive-semidefinite-preserving cones
نویسندگان
چکیده
منابع مشابه
Completely Positive Semidefinite Rank
An n×n matrix X is called completely positive semidefinite (cpsd) if there exist d×d Hermitian positive semidefinite matrices {Pi}i=1 (for some d ≥ 1) such that Xij = Tr(PiPj), for all i, j ∈ {1, . . . , n}. The cpsd-rank of a cpsd matrix is the smallest d ≥ 1 for which such a representation is possible. In this work we initiate the study of the cpsd-rank which we motivate twofold. First, the c...
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A well-known result of Lyapunov on continuous linear systems asserts that a real square matrix A is positive stable if and only if for some symmetric positive definite matrix X, AX + XA is also positive definite. A recent result of Moldovan-Gowda says that a Z-matrix A is positive stable if and only if for some symmetric strictly copositive matrix X, AX + XA is also strictly copositive. In this...
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A real symmetric matrix M is completely positive semidefinite if it admits a Gram representation by positive semidefinite matrices (of any size d). The smallest such d is called the 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 show that if such an upper bound exists, it has to be a...
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For a closed cone C in Rn, the completely positive cone of C is the convex cone K in Sn generated by {uuT : u ∈ C}. Completely positive cones arise, for example, in the conic LP reformulation of a nonconvex quadratic minimization problem over an arbitrary set with linear and binary constraints. Motivated by the useful and desirable properties of the nonnegative orthant and the positive semidefi...
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ژورنال
عنوان ژورنال: Linear Algebra and its Applications
سال: 1984
ISSN: 0024-3795
DOI: 10.1016/0024-3795(84)90127-7