Editing Bilinear form (section)

==Associated quadratic form==
{{further|Quadratic form#Definitions}}
For any bilinear form {{math|''B'' : ''V'' × ''V'' → ''K''}}, there exists an associated [[quadratic form]] {{math|''Q'' : ''V'' → ''K''}} defined by {{math|''Q'' : ''V'' → ''K'' : '''v''' ↦ ''B''('''v''', '''v''')}}.

When {{math|char(''K'') ≠ 2}}, the quadratic form ''Q'' is determined by the symmetric part of the bilinear form ''B'' and is independent of the antisymmetric part.  In this case there is a one-to-one correspondence between the symmetric part of the bilinear form and the quadratic form, and it makes sense to speak of the symmetric bilinear form associated with a quadratic form.

When {{math|1=char(''K'') = 2}} and {{math|dim ''V'' > 1}}, this correspondence between quadratic forms and symmetric bilinear forms breaks down.