|Definition:|| function f that attributes a scalar to any pair of vectors U and V in a given vector space, with the following properties: |
- and where α and β are scalars,
- and for any vector W existing in the same vector space
Note 1 to entry: A bilinear form over an n-dimensional vector space can be represented by a square matrix and the scalar is .
Note 2 to entry: The bilinear forms over a given n-dimensional vector space constitute an -dimensional vector space.
Note 3 to entry: The concept of bilinear form extends to "linear form" in the case of one vector and to "multilinear form" (or m-linear form) in the case of an ordered set of m vectors.