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## Main Question or Discussion Point

Hello! I read about this in several place, but I haven't found a really satisfying answer, so here I am. As far as I understand, non-coordinate basis are mainly obtained from coordinate basis, by making the system orthonormal. For example the unit vector in polar coordinates in the direction of ##\theta## gets a factor of ##1/r## to make it orthonormal. I am a bit confused about the difference between the 2 types of basis. To me they seem equivalent in the sense that you can easily go from one to another by doing the right transformation. So beside the fact that one is more useful than the other, depending on the calculations, what is the fundamental difference between them? I am sure I am missing something, but I can't really see why they are so different conceptually.