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arXiv · 2608.08242

Bang--bang representation of $3\times 3$ embeddable stochastic matrices

Leonel Robert
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Abstract

We prove that every embeddable $3\times3$ row-stochastic matrix is a product of at most seven elementary row-stochastic matrices. Frydman's example shows that this bound is sharp. The proof combines Frydman's six-factor criterion and spiral theorem with a reduction to a three-parameter critical family and an analysis of the membership certificates that persist along it.

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Leonel Robert. 2026-08-08. Bang--bang representation of $3\times 3$ embeddable stochastic matrices. https://arxiv.org/abs/2608.08242

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