Given a basis A = {a1,a2...an} we can always translate coordinates originally expressed with this basis to another basis A' = {a1',a2'...an'}. To do this we simply do some matrix-multiplication and it turns out that the change of basis matrix equals a square matrix whose rows are the coordinates of the original basis vectors written in terms of the new basis-vectors. I'm finding this a little hard to understand intuitively - can someone give me an example from maybe R^2 that shows why this is in an intuitive manner.(adsbygoogle = window.adsbygoogle || []).push({});

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# Change of basis matrix

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