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The process of alternately row scaling and column scaling a positive $n\times n$ matrix $A$ converges to a doubly stochastic positive $n \times n$matrix $S(A)$, often called the \emph{Sinkhorn limit} of $A$. The main resultin this paper is the computation of exact formulae for the Sinkhorn limits ofcertain symmetric positive $3\times 3$ matrices.

Matrix scaling and explicit doubly stochastic limits