convex combination

Thus, the line segment can be expressed as a convex combination of the segment's two end points.

The set of all convex combinations of points in X.

As a particular example, every convex combination of two points lies on the line segment between the points.

Weighted means are functionally the same as convex combinations, but they use a different notation.

Such a linear combination is called a convex combination.

A vector of this type is known as a convex combination of .

All convex combinations are within the convex hull of the given points.

Alpha blending is a convex combination of two colors allowing for transparency effects in computer graphics.

Mixed ensembles are decomposable into a convex combination of different ensembles.

Pure ensembles cannot be decomposed as a convex combination of different ensembles.

Savage assumed that it is possible to take convex combinations of decisions and that preferences would be preserved.

Geometrically, when the state is not expressible as a convex combination of other states, it is a pure state.

Any convex combination or mixture distribution of iid sequences of random variables is exchangeable.

If is not a vertex itself, it must be the convex combination of vertices of , say .

Affine combinations are like convex combinations, but the coefficients are not required to be non-negative.

It follows from the spectral theorem for compact self-adjoint operators that every mixed state is an infinite convex combination of pure states.

The first assumption is that in the case where the background is opaque (i.e. ), the over operator represents the convex combination of and :

Thus, the zoo-keeper's preferences are non-convex: The zoo-keeper prefers having either animal to having any strictly convex combination of both.

The convex combination formed by the points CEG is a triangle, and represents the "center of effect" of the three pitches.

The convex hull of a finite point set is the set of all convex combinations of its points.

The simplex is convex, and any point within the simplex is a convex combination of the vertices.

Starting with a formulation of the pitch spiral, inner spirals are generated by a convex combination of points on outer spirals.

It can regarded as the convex combination of , a maximally entangled state, and identity, the maximally mixed state.

We know that is opaque and thus follows that is opaque, so in the above equation, each operator can be written as a convex combination:

In fact, the collection of all such convex combinations of points in the set constitutes the convex hull of the set.