- #1

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[tex]Hom_{K}(V,K) \otimes Hom_{K}(V,K)[/tex] and [tex]Hom_{K}(V \otimes V,K)[/tex]

where K is a field and V is a vector space over K.

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- Thread starter antonio85
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- #1

- 5

- 0

[tex]Hom_{K}(V,K) \otimes Hom_{K}(V,K)[/tex] and [tex]Hom_{K}(V \otimes V,K)[/tex]

where K is a field and V is a vector space over K.

- #2

quasar987

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For V,W vectors spaces over K, and o the tensor product,

(1) Hom(V,W) is naturally isomorphic to V* o W

(2) V o K is naturally isomorphic to V

(3) (V o W)* is naturally isomorphic to V* o W*

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