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- Feb 6th 2009, 07:19 AMszpengchaoA proof regarding rank
- Feb 6th 2009, 08:30 AMMush
- Feb 6th 2009, 08:40 AMszpengchaolinear algebra
they r linear maps from V to W.

- Feb 6th 2009, 02:47 PMHallsofIvy
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 ?

- Feb 6th 2009, 03:02 PMszpengchaook.
wait. please check my proof:

so it is equivalent to prove: