Matrix scaling and explicit doubly stochastic limits

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 $S(A)$, often called the \emph{Sinkhorn limit} of $A$. The main result in this paper is the computation of exact formulae for the Sinkhorn limits of certain symmetric positive $3\times 3$ matrices.

18 pages. This article is a shortened version of arXiv:1902.04544 and has been accepted to appear in The Journal of Linear Algebra and its Applications

References in corpus (3)

• A review of matrix scaling and Sinkhorn's normal form for matrices and positive maps
• Alternate minimization and doubly stochastic matrices
• Answers to Some Questions about Explicit Sinkhorn Limits posed by Mel Nathanson