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schwarzschild
Jul20-10, 12:30 PM
Are the following three equivalent?

P_{\alpha}A^{\beta}\tilde{\omega}^{\beta}(\vec{e_{ \beta}} ) = \sum_{\alpha = 0}^{3}{P_{\alpha}\tilde{\omega}^{\alpha}(\sum_{\be ta = 0}^{3}{A^{\beta}\vec{e}_{\beta}) = \sum_{\alpha = 0}^{3}{P_{\alpha}A^{\alpha}

Fredrik
Jul20-10, 12:40 PM
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.

George Jones
Jul20-10, 01:00 PM
Don't use two sets of tex /tex tags; enclose the whole equality in one set of tex /tex tags.