Visualizing Change Of Basis Dynamically

How can we visualize a B-coordinate system not from the "standard" way, but from the perspective of the B-basis, itself? Further, if we apply the Change-Of-Basis transformations that we've computed previously, what does that "look" like? Answering these two questions simultaneously gives us a nice, dynamic, visual way of understanding what is going on with the Change of Basis Formula

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Now it's your turn:
1) Summarize the big idea of this video in your own words
2) Write down anything you are unsure about to think about later
3) What questions for the future do you have? Where are we going with this content?
4) Can you come up with your own sample test problem on this material? Solve it!

Learning mathematics is best done by actually DOING mathematics. A video like this can only ever be a starting point. I might show you the basic ideas, definitions, formulas, and examples, but to truly master math means that you have to spend time - a lot of time! - sitting down and trying problems yourself, asking questions, and thinking about mathematics. So before you go on to the next video, pause and go THINK.

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This video was created by Dr. Trefor Bazett, an Assistant Professor, Educator at the University of Cincinnati.

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[ceejay]

You explain things VERY CLEARLY. Thank you

[SpartaSpartan]

I've been trying to visualize this in my head for several days, this nailed it!

[awazin]

It's amazing how you can turn something complex and abstract into a simple and concrete example. Thanks again :)

[briandwi]

I have watched this set of videos a good few times because you completely understand what is going on. The ideas expressed are very elegant but tricky to really internalise. Your explanation and the animations are a fantastic aid to understanding. Brilliant stuff Dr Trefor, just brilliant.

[mojtabavahdati]

This video is PhEnOmEnAl, one of the coolest and smartest ones I've seen on YouTube! Really, the likes must be waaay more! ;(
Thank you a TON anyways!

[RupayanHalder-ec]

As beginer of linear algebra like me this video is really helpful for understanding.

[ekalavyain]

Sir can you do bessel function and tensors of rank 2.

[SabrinaXe]

I don’t understand if someone from the C basis sees their basis as straight but we from the standard basis see their basis as tilted, then do the people from C basis “interpret straight” different to what we interpret as straight ? Is that where the difference is coming from?

[alfcnz]

Okay, now I need to code this up myself. It is still so blurry… Dang…

[ccuuttww]

The calculation don't show the tween motion u have to imagine by yourself which is upset

[andrei]

jeez you took your acting classes too seriously

[rogerwood]

Does a lot of talking but sez very little.