Bilinear Forms

  • K. W. Gruenberg
  • A. J. Weir
Part of the Graduate Texts in Mathematics book series (GTM, volume 49)


Let V be a vector space over a field F. A bilinear form σ on V is a mapping of the ordered pairs of vectors of V into F such that
$$ \begin{gathered} {\text{B}}.1.{\text{ }}\sigma (xa + yb,c) = x\sigma (a,c) + y\sigma (b,c), \hfill \\ {\text{B}}.2.{\text{ }}\sigma (a,xb + yc) = x\sigma (a,b) + y\sigma (a,c), \hfill \\ \end{gathered} $$
for all vectors a, b, c in V and all scalars x, y in F.


Bilinear Form Vector Space Versus Projective Geometry Symmetric Bilinear Form Ground Field 
These keywords were added by machine and not by the authors. This process is experimental and the keywords may be updated as the learning algorithm improves.


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Copyright information

© Springer Science+Business Media New York 1977

Authors and Affiliations

  • K. W. Gruenberg
    • 1
  • A. J. Weir
    • 2
  1. 1.Department of Pure Mathematics, Queen Mary CollegeUniversity of LondonEngland
  2. 2.School of Mathematical and Physical SciencesUniversity of SussexEngland

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