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Let V be a vector space over k, and let B be a bilinear map into k,

i.e.:

B:VxV-->k

Define the left-kernel of B to be the set of A in V with

B (A,v)=0 for all v in V,

and define the right-kernel similarly.

Question: what relation is there between the two kernels , as subspaces

of V?

I am pretty sure the answer has to see with the tensor product V(x)V;

but I am not sure of how to express the dual of VxV in terms of the tensor

product. Any ideas?

Thanks.

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# Left- and Right- Kernels of Bilinear maps B:VxV->K for V.Spaces

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