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Originally Posted by szpengchao 'rank' is a very broad word and has many different meanings in different topics in mathematics. What topics are you talking about and what do alpha and beta represent?
they r linear maps from V to W.
So the "rank" of is the dimension of as a subspace of W. If w is in then there exist v in V such that is in W. Certainly that is true if and are in W. Do you see why that means that must be a subspace of the direct sum and ?
wait. please check my proof: so it is equivalent to prove:
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