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Possible Duplicate:
Understanding isomorphic equivalences of tensor product

I have the following question: Let $V$ be a vectorspace with an inner product $<.,.>$. Let $V^{*}$ be its dual. Is it true that $V \otimes V^{*} = End(V)$ ? If yes in which way ? what is the isomorpism ? Thanks in advance.

mika

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    It is only true if $V$ is finite-dimensional.2012-05-25
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    is there any coordinate free isomorphism ?2012-05-25
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    @mika Dear mika, I believe the definition of the isomorphism in the question I linked is coordinate-free. To prove that it _is_ an isomorphism it seems to me that you must choose a basis, since the result may not be true outside of the finite case. I can add more detail there, if you like. Cheers,2012-05-25
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    sure. thanks a lot.2012-05-25

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