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Summation Notation

  1. Jul 20, 2010 #1
    Are the following three equivalent?

    [tex] P_{\alpha}A^{\beta}\tilde{\omega}^{\beta}(\vec{e_{\beta}} ) [/tex] [tex]= \sum_{\alpha = 0}^{3}{P_{\alpha}\tilde{\omega}^{\alpha}(\sum_{\beta = 0}^{3}{A^{\beta}\vec{e}_{\beta}) = \sum_{\alpha = 0}^{3}{P_{\alpha}A^{\alpha} [/tex]
     
    Last edited: Jul 20, 2010
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  3. Jul 20, 2010 #2

    Fredrik

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    The second equality is correct, assuming that the omegas are dual basis vectors. The first expression doesn't make sense, but it looks like a typo. Change the second beta to an alpha, and the first equality is good too.
     
  4. Jul 20, 2010 #3

    George Jones

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    Don't use two sets of tex /tex tags; enclose the whole equality in one set of tex /tex tags.
     
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