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Change of basis makes sense: the change of basis formula explained simply

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This video is part of a linear algebra series:
Vectors and Bases: https://youtu.be/3ZfrJ0Sk5iY
Matrices and Linear Transforms: https://youtu.be/CBIO4xJ1Cok
Matrix inverses: https://youtu.be/ESKcF8XFzLM



This video is about changing the basis (or coordinate system) of a matrix or a vector. While the change of basis formula is often presented as something to just memorise, we'll see it's actually very very straightforward.


Hints for homework:
1. You can do it! Think about what it does to the basis vectors!

2. Remember, in the original case you first translate the input vector from Bob's basis to Alice's so you can apply M_a, then translate back. A similar idea applies, but you need to translate to something M_a can take as input.

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