Where does the gamma factor in Lorentz transformations come from?

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Lizwi
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In Lorentz transformation, where does factor Gamma [itex]\frac{1}{\sqrt{1-\frac{v^{2}}{c^{2}}}}[/itex] comes from?
 

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It comes from the fact that you want an inverse transform to exist. So if I call L(v) my Lorentz transformation, then when I require that L(-v)L(v) x = x, this fixes the "normalization".