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bilinear form

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linear functional on tensor product square of a vector space

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Bilinear forms
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In mathematics, a bilinear form is a bilinear map V × V → K on a vector space V (the elements of which are called vectors) over a field K (the elements of which are called scalars). In other words, a bilinear form is a function B : V × V → K that is linear in each argument separately:

B(u + v, w) = B(u, w) + B(v, w)     and     B(λu, v) = λB(u, v)

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