Probability simplex
= Probability simplex
{title2=$\Delta_n=\{x\in\mathbb R^n:x\ge0,\ \mathbf1^Tx=1\}$}
The probability simplex consists of vectors of nonnegative weights summing to one. It is the <convex hull> of the coordinate vectors. A <linear function> $r^Tx$ has maximum $\max_i r_i$ on this simplex; equality holds exactly when the weights are supported on maximizing indices.