# What are applications of Frobenius inequality?

Frobenius inequality states that $\mathrm{rank} AB + \mathrm{rank} BC \leq \mathrm{rank} ABC + \mathrm{rank} B$ whenever this has a meaning. I remember being told that this was sometimes useful. Do you know of any example?

Thank you.

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Thanks but I can't read it. :( –  timofei Oct 15 '11 at 20:35