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 to understand.

Hints for homework:

1. You can do it! Think about what it does to the basis vectors!

- 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.