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Let Vand W be vector spaces over F, and let B( V, W) be the...

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Advance Math

Let Vand W be vector spaces over F, and let B( V, W) be the setof all bilinear forms f: V x W ~ F. Show that B( V, W) is asubspace of the vector space of functions 31'( V x W).

Prove that the dual space B( V, W)* satisfies the definition oftensor product, with respect to the bilinear mapping b: V x W ->B( V, W)* defined by b(v, w)(f) =f(v, w), f E B(V, W), V E V, W EW.

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