After the thanksgiving break, I thought I could come back to teach synchronous lectures again but it looks unlikely. There are two things that we have to learn and they are eigenthings and inner products.
For eigenvectors and eigenspaces, I strongly recommend the following video the following video by Courtney Gibbons: https://youtu.be/egrduM4j9bA This should give you an idea about what everything is all about. If you are interested, you can also watch how to find Fibonacci numbers using diagonalization in this video: https://youtu.be/0lZMNwkq42M .
There is also Tom Roby's channel:
You should watch all the videos from the Eigensystems Playlist and the videos G1-G6 from the Inner Producs playlist.