Are the following three equivalent?(adsbygoogle = window.adsbygoogle || []).push({});

[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]

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# Summation Notation

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