Hi, all: 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.