An

convex combination of a

sequence of

vectors

**v**_{1},

**v**_{2}, ...,

**v**_{n} is given by

*c*_{1}**v**_{1} + *c*_{2}**v**_{2} + ... + *c*_{n}**v**_{n}

where

*c*_{1},

*c*_{2}, ...,

*c*_{n} are

real numbers with the restriction that

*c*_{1} +

*c*_{2} + ... +

*c*_{n} = 1 and

*c*_{1} __>__ 0,

*c*_{2} __>__ 0, ... ,

*c*_{n} __>__ 0.

For example, a convex combination of a set of points in 3-space is always some point in the convex hull of those points.