All doubly stochastic solutions to $AXA=XAX$ when $A$ is a permutation matrix

Bogdan D. Djordjević, Nebojša Č. Dinčić, Yingshan Chen

In this paper we obtain all doubly-stochastic solutions to the Yang-Baxter-like matrix equation $AXA=XAX$ when $A$ is a permutation matrix. We characterize the permutation soluti…