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Possible Duplicate:
How do you prove $\def\rank{\operatorname{rank}}\rank(f_3 \circ f_2) + \rank(f_2 \circ f_1) \leq \rank(f_3 \circ f_2 \circ f_1) + \rank(f_2) $?

The Frobenius inequality of linear algebra, with $A,B,C\in M_n(\mathbb{F})$, is: $$\operatorname{rank}{AB}+\operatorname{rank}{BC}\le\operatorname{rank}{B}+\operatorname{rank}{ABC}$$

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    In wikipedia, I've already read the proof you referred to. What I don't understand is, what is $\ker{ABC}/\ker{BC}$ and why that projection is one-to-one?2012-09-19
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    This is also a duplicate of http://math.stackexchange.com/questions/497830/frobenius-inequality-rank .2016-07-23

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