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- February 6th 2009, 06:19 AMszpengchaoA proof regarding rank
- February 6th 2009, 07:30 AMMush
- February 6th 2009, 07:40 AMszpengchaolinear algebra
they r linear maps from V to W.

- February 6th 2009, 01:47 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 ?

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

so it is equivalent to prove: