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.
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.
The prove of Frobenius inequality plays very important role in linear algebra's problem. you also see PROBLEMS AND THEOREMS IN LINEAR ALGEBRA by V. Prasolov (www.amazon.com/Problems-Theorems-Translations-Mathematical-Monographs/dp/0821802364)