Source: /cirosantilli/bilinear-form

= Bilinear form
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Analogous to a <linear form>, a bilinear form is a <Bilinear map> where the <image (mathematics)> is the <underlying field of the vector space>, e.g. $\R^n \times \R^m \to \R$.

Some definitions require both of the input spaces to be the same, e.g. $\R^n \times \R^n \to \R$, but it doesn't make much different in general.

The most important example of a bilinear form is the <dot product>. It is only defined if both the input spaces are the same.