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Change of basis

7 videos
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!

Coordinates with respect to a basis

VIDEO 16:08 minutes
Understanding alternate coordinate systems

Change of basis matrix

VIDEO 17:55 minutes
Using a change of basis matrix to get us from one coordinate system to another.

Invertible change of basis matrix

VIDEO 13:34 minutes
Using an invertible change of basis matrix to go between different coordinate systems

Transformation matrix with respect to a basis

VIDEO 18:02 minutes
Finding the transformation matrix with respect to a non-standard basis

Alternate basis transformation matrix example

VIDEO 13:20 minutes
Example of finding the transformation matrix for an alternate basis

Alternate basis transformation matrix example part 2

VIDEO 12:36 minutes
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 coordinate systems to help find a transformation matrix

VIDEO 28:59 minutes
Changing our coordinate system to find the transformation matrix with respect to standard coordinates