Convex combination

A convex combination is a special kind of Linear combination where all of the coefficients are non-negative and their sum is one. Mathematically, it reads

α1v1+...+αnvnwhereα1,…,αn≥0andα1+…+αn=1\alpha_{1}v_{1}+...+\alpha_{n}v_{n}\quad\text{where}\quad \alpha_{1},\ldots,\alpha_{n}\geq 0\quad\text{and}\quad \alpha_{1}+\ldots+\alpha_{n}=1

These are common in Probability theory (and by extension quantum mechanics), as the constraints on the coefficients are the same as the ones put on a set of probabilities, namely that probabilities must be non-negative and that they must sum to one.