Matrix scaling, explicit Sinkhorn limits, and arithmetic

Melvyn B. Nathanson

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arXiv · 1902.04544

Matrix scaling, explicit Sinkhorn limits, and arithmetic

Melvyn B. Nathanson

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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.

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Melvyn B. Nathanson. 2019-02-12. Matrix scaling, explicit Sinkhorn limits, and arithmetic. https://arxiv.org/abs/1902.04544

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