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Prove that change of basis matrix is always invertible
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Prove that change of basis matrix is always invertible

User Dwc
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Answer:

The only way for this to happen is if BA=In is the identity. The same argument, now interpreting ei as [wi]β2, shows that AB is also the identity. So A and B are both invertible. So every change-of-basis matrix is necessarily invertible if you think about it carefully.

User PaulG
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