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 ?
Then we always have C = UH where H is positive semidefinite and positive definite if C has full rank, and U is [m.
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.
A], i(x)) is positive semidefinite for all x [member of] U [intersection] A;
Determination of the critical point as the limiting stable state of the system requires a positive semidefinite quadratic form of its description, where you can find vector [DELTA]n complying with Equation (8).
Duality for various forms of mathematical problems involving square roots of positive semidefinite quadratic forms has been discussed by many authors [10,23-25].
v] is a positive semidefinite matrix, (12) will be a convex optimization problem which can be solved by the CVX MATLAB toolbox [24].
Let T: H [right arrow] H be an autoadjoint, positive semidefinite, linear operator and let A be the matrix of T, relative to an arbitrary basis.
omega]] (A) we consider A a symmetric positive semidefinite matrix so [a.
The mass matrix is positive definite (all its eigenvalues are positive), and the stiffness and damping matrices are positive semidefinite (all their eigenvalues are nonnegative).
MATHEMATICAL EXPRESSION NOT REPRODUCIBLE IN ASCII] is a positive semidefinite (2 x 2) matrix that contains the variances and covariances of the residuals of the value and growth portfolio excess returns in state [S.