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- Thread starter FilipVz
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- Thread starter
- #1

- Feb 5, 2012

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- Feb 15, 2012

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An isomorphism is, among other things, a bijection. So all one needs to do is show 2 things:

1) A linear injection preserves linear independence

2) A linear surjection preserves spanning

These two facts together show that the image under our given isomorphism of a basis for the first vector space is a basis for the second space, and since the isomorphism is bijective, they have the same cardinality.