Two-coordinate stochastic averaging
= Two-coordinate stochastic averaging
{title2=$\begin{pmatrix}t&1-t\\1-t&t\end{pmatrix},\quad0\leq t\leq1$}
= T-transform of two coordinates
{c}
{synonym}
This <doubly stochastic matrix> replaces two values $a,b$ by $ta+(1-t)b$ and $(1-t)a+tb$, preserving their sum. It fixes all other coordinates when embedded in a larger <matrix>. A finite product of such averaging <matrices> and <permutation matrices> is again doubly stochastic.