positive definite


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positive definite

[′päz·əd·iv ′def·ə·nət]
(mathematics)
A square matrix A of order n is positive definite if for every choice of complex numbers x1, x2, …, xn , not all equal to 0, where x̄j is the complex conjugate of xj .
A linear operator T on an inner product space is positive definite if 〈 Tu, u 〉 is greater than 0 for all nonzero vectors u in the space.
References in periodicals archive ?
In the sequel we use for simplicity the term quasi-definite linear functional (positive definite linear functional) for linear functionals that are quasi-definite (positive definite) on the space of polynomials of sufficiently large degree.
It is clear that [C.sub.k], [C.sup.*.sub.k], [C.sub.d], and [C.sup.*.sub.d] are positive definite and [C.sub.h], [C.sub.hk], and [C.sub.hd] are nonnegative definite.
Given a positive definite matrix R and three positive constants [c.sub.1], [c.sub.2], [T.sub.f] ([c.sub.1] < [c.sub.2]), the polynomial fuzzy system (3) with control input u(t) is said to be finite-time stabilization with respect to [mathematical expression not reproducible].
if [rho](A) < 1, C is a fixed positive definite matrix, matrix H solves the corresponding Lyapunov matrix equation (5), and
Equation (15) is a matrix Lyapunov equation where matrices P and Q are positive definite matrices.
If [A.sub.d] is positive definite and E is negative definite or [A.sub.d] is negative definite and E is positive definite, then the S-system in (1) is stable.
The Ghost-Fluid Method leads to a symmetric positive definite linear systems that captures the discontinuity in the normal derivative while smearing out the discontinuity in the tangential direction to the interface.
where S [member of] [R.sup.nxn] is a positive definite symmetric matrix and T [member of] [R.sup.nxn] is a unity upper triangular matrix.
In classical analysis a complex valued continuous function is said positive definite (resp.
If there exists symmetric positive definite matrix Q, such that the following LMI holds:
For two symmetric matrices of the same dimensions X and Y, X > Y means that X-Y is positive definite. [R.sup.+] is the set of positive real numbers.