Up Vector Trick Part 2 (Maya Matrices)

So in case anybody wanted to look into how the up vector trick works internally I thought I would make a post with links to the tutorials and resources I found helpful when learning about using matrices in Maya.

What is a Vector:

Here is a great animated explanation: https://www.youtube.com/watch?v=fNk_zzaMoSs

Here is another animated explanation: https://www.youtube.com/watch?v=bOIe0DIMbI8

How do Vectors Work in Maya:

Maya Matrices: https://www.youtube.com/watch?v=MmQ46OFSiYo (the most important part is about 5 minutes in)

More Maya Matrices: http://www.kimonmatara.com/hands_on_matrices/

Explanation of basis vectors: https://www.youtube.com/watch?v=k7RM-ot2NWY

Transformations: https://www.youtube.com/watch?v=kYB8IZa5AuE