In mathematics, positive semidefinite may refer to:

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Positive-definite function

In mathematics, a positive-definite function is, depending on the context, either of two types of function. Let R {\displaystyle \mathbb {R} } be the set

Definite matrix

"leading" is removed. Positive-definite and positive-semidefinite real matrices are at the basis of convex optimization, since, given a function of several real

Definite quadratic form

negative-definite. A semidefinite (or semi-definite) quadratic form is defined in much the same way, except that "always positive" and "always negative"

Semidefinite programming

(a user-specified function that the user wants to minimize or maximize) over the intersection of the cone of positive semidefinite matrices with an affine

Wigner quasiprobability distribution

transform, to yield the Husimi representation, below), results in a positive-semidefinite function, i.e., it may be thought to have been coarsened to a semi-classical

Convex function

differentiable function of several variables is convex on a convex set if and only if its Hessian matrix of second partial derivatives is positive semidefinite on

Hessian matrix

Hessian is positive-semidefinite, and at a local maximum the Hessian is negative-semidefinite. For positive-semidefinite and negative-semidefinite Hessians

Gaussian process

non-negative definite covariance function K {\displaystyle K} and let R {\displaystyle R} be a symmetric and positive semidefinite function. Then, there exists a