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arXiv · 1903.06778

Matrix scaling limits in finitely many iterations

Melvyn B. Nathanson
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Abstract

The alternate row and column scaling algorithm applied to a positive $n\times n$ matrix $A$ converges to a doubly stochastic matrix $S(A)$, sometimes called the \emph{Sinkhorn limit} of $A$. For every positive integer $n$, a two parameter family of row but not column stochastic $n\times n$ positive matrices is constructed that become doubly stochastic after exactly one column scaling.

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Melvyn B. Nathanson. 2019-03-15. Matrix scaling limits in finitely many iterations. https://arxiv.org/abs/1903.06778

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