positive semidefinite


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positive semidefinite

[′päz·əd·iv ¦sem·i′def·ə·nət]
(mathematics)
Also known as nonnegative semidefinite.
A square matrix A is positive semidefinite if for every choice of complex numbers x1, x2, …, xn , where x̄j is the complex conjugate of xj .
A linear operator T on an inner product space is positive semidefinite if 〈 Tu, u 〉 is equal to or greater than 0 for all vectors u in the space.
References in periodicals archive ?
SDP problems arise from the well-known linear programming problems by replacing the vector of variables with a symmetric matrix and replacing the non-negativity constraints with positive semidefinite constraints.
Setting M= I and N = S leads to a P-regular splitting where N is non-Hermitian positive semidefinite and [rho]([M.
between two symmetric matrices (of the same order) mean that B - A is positive semidefinite or positive definite, respectively.
3) have the unique symmetric, positive semidefinite solutions which define the proper controllability and observability Gramians of the descriptor system (1.
This matrix F is rank-1 symmetric positive semidefinite with eigenvalues [lambda] = 0 and [lambda] = 1 + f[(x).
We call an n x m-matrix H A-related if AH is symmetric positive semidefinite (s.
Suppose that F is symmetric positive semidefinite with nullity r.
The support [sigma](A, B) of a matrix pencil (A, B) is the smallest number [tau] such that [tau]B - A is positive semidefinite.
By virtue of the addition theorem, one can directly see that the symmetric positive semidefinite matrix [[PHI].
It is known how to bound the constants in the weak approximation property when the system matrix is given as the sum of positive semidefinite local matrices.