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If i understand it correctly, change of basis is just a specific case of a linear transformation. Specifically given a vector space $V$ over a field $F$ such that $\dim V=n$, change of basis is just a transformation from $F^n$ to $F^n$. Does change of basis in and of itself have practical uses that are separate from linear transformations? What I mean is separate from linear transformations that do more than just change the basis of a vector in it's own vector space.

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    @Asaf Karagila - Nu, I'm waiting for your answer :-)2012-06-11
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    Note: Change of bases must be **invertible** transformations $F^n\to F^n$.2012-06-11
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    While the technical/computational aspects of a change of basis is largely given by the study of linear transformations in general, there are some _philosophical_ distinctions that can be drawn. A nice description is given [by Terry Tao on his blog/buzz](https://profiles.google.com/114134834346472219368/buzz/AWqcUGXVjcs).2012-06-12

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