How to show that two vector spaces $V$ and $W$ are the same, if we know $\dim V = \dim W$ and $V$ is a subspace of $W$ ? Would it suffice to show there exists an isomorphism between them ? Any help would be much appreciated.
How to show that two vector spaces $V$ and $W$ are the same
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0Thanks guys would keep that in mind for future questions. – 2012-02-07
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Assuming the dimensions are finite, show that a basis of $V$ is a basis of $W$.
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0Cool, thanks for that tip so a basis B = {x1, x2 ... xn} of$V$can span all of V, but since$W$is also of the same dimension hence the same basis B can span all of$W$as well as the subspace must be because of the restriction on the scalar coefficients of V's vectors ? Now sure if that was the best way to express it though ? – 2012-02-07