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Change of basis
Finding a coordinate system boring. Even worse, does it make certain transformations difficult (especially transformations that you have to do over and over and over again)? Well, we have the tool for you: change your coordinate system to one that you like more. Sound strange? Watch this tutorial and it will be less so. Have fun!
Understanding alternate coordinate systems
Using a change of basis matrix to get us from one coordinate system to another.
Using an invertible change of basis matrix to go between different coordinate systems
Finding the transformation matrix with respect to a non-standard basis
Example of finding the transformation matrix for an alternate basis
Showing that the transformation matrix with respect to basis B actually works. Brief point on why someone would want to operate in a different basis to begin with.
Changing our coordinate system to find the transformation matrix with respect to standard coordinates