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I am having a little trouble with the difference between a covariant vector and contravariant vector. The examples that I come across say that an example of a contravariant vector is velocity and that a contravariant must contra-vary with a change of basis to compensate.

So if you have a velocity that is measured in m/s and you want to measure it in km/s then the velocity shrinks. Is that because you increased the co-ordinate system to km and so that velocity must shrink to compensate for that increase? Or am I thinking of it the wrong way?

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# Covariant versus Contravariant

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