Multilinear map

Bilinear form

A bilinear form is a multilinear map from a vector space to its underlying field , #m/def/linalg i.e. linear in both arguments separately

Further terminology

• A bilinear form is called symmetric iff .
• A bilinear form is called nondegenerate iff is an isomorphism, equivalently for all implies .

Properties

• Correspondence between quadratic forms and symmetric bilinear forms away from 2

See also

• Quadratic space

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