Viewing topic: Bilinear Form

See sub-topics for Bilinear Form ... >> Mathematics >> Abstract Algebra >> Bilinear Form

Highest Rated Sign

No video has been submitted for this term

Nobody has posted a sign yet.

Bilinear Form

  • Definition: Let V be a real vector space. A bilinear form on V is a real-valued function of two vector variables - a map VxV -> R. Given a pair v, w of vectors, the form returns a real number that will usually be denoted by <v,w>. A bilinear form is required to be linear in each variable: <rv1,w1> = r<v1,w1> and <v1+v2,w1> = <v1,w1> + <v2,w1>; <v1,rw1> = r<v1,w1> and <v1,w1+w2> = <v1,w1> + <v1,w2>.

    Source: Algebra, second edition by Michael Artin

  • There are no comments for this topic.