Matrix scaling, explicit Sinkhorn limits, and arithmetic

Abstract

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 $S(A)$, called the \emph{Sinkhorn limit} of $A$. Exact formulae for the Sinkhorn limits of certain symmetric positive $3\times 3$ matrices are computed, and related problems in diophantine approximation are considered.

29 pages

References in corpus (1)

• A review of matrix scaling and Sinkhorn's normal form for matrices and positive maps