Writing Vectors in a New Coordinate System **Example**

The best method to algebraically express a vector in some given coordinate system (ie in terms of a given basis) is by introducing a matrix whose columns are the basis vectors, and then inverting that. We pick up some new notation along the way.

**************************************************
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.

***************************************************
Want more ideas for learning math effectively?
►How to Watch Math Videos:

****************************************************
►Want some cool math? Check out my "Cool Math" Series:

****************************************************
Course Playlists:

*****************************************************
*****************************************************

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

BECOME A MEMBER:

MATH BOOKS & MERCH I LOVE:

[briaschraeder]

This wonderful fall I am teaching myself linear algebra for a virtual math independent study... I cannot tell you how grateful I am for these videos. No other mode of learning was working for me until I started your series. Cheers :)

[confused]

After going through all the previous lectures I was not able to glue these concepts: Span, Basis Vector, inverse Matrix, RRF, R and constant vector.
Only after this lecture, I now fully understand what the heck they are and the relationship between them.
It was like learning what all the components of a car are. Only when I successfully assemble them into a car, then it is an "aha" moment for me.,
Thank you so much Dr. Trefor 👍

[TonyWayne]

Holy crap! I didn't know you tackled linear algebra too I thought you only taught discreet math 😭this is the most incredible news ever i only passed discreet math because of your youtube videos and now i can safely say i will pass my linear algebra final too :D I'm beyond hype, Thanks Dr.!

[sounakroy]

When you say x vector can be written as the product of P(sub)B matrix and the vector x interms of B basis. x= P(sub)b • [x]sub b, is the x on the left hand side written in terms of e1 and e2?

[youssefdirani]

I wish I can be of any help to you Dr. sometime