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Contraction distributive property in GA

  1. Jun 5, 2009 #1
    Hello,
    according to my book of 'Geometric Algebra' the operation of Left-Contraction for Blades has a distributive property in respect to addition. However the authors do not prove it, nor they give the smallest hint on how to derive it.

    The property says that:

    [tex](\textbf{A+B})|\textbf{C}=\textbf{A}|\textbf{C}+\textbf{B}|\textbf{C}[/tex]

    where the symbol | denotes Left-Contraction.
    Does anyone have a clue on how to prove that identity?
     
  2. jcsd
  3. Jun 11, 2009 #2
    Apparently the answer should be that the left contraction is constructed axiomatically by using the operations [tex]\wedge[/tex] (wedge product) and [tex]\ast[/tex] (scalar product), which are both bilinear. It follows, that the left-contraction must be bilinear too.
     
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