Youtor
Visualizing Diagonalization amp Eigenbases
>> YOUR LINK HERE: ___ http://youtube.com/watch?v=EJG6gBeVdfw
Diagonal transformations are really nice to visualize geometrically. In 2D they are just a combination of horizontal and vertical stretching. • While a generic matrix isn't quite this nice, if you can find a basis of eigenvectors, then the transformation looks like stretching and compressing along those eigenvectors by the values of the eigenvectors. This makes it pretty nice, but we can do better. • When we diagonalize a matrix, this is a composition of transformations. You first apply a change-of-basis to convert from the standard basis to the eigenbasis. Then you apply the nice diagonal transformation. Finally, you convert back. • • ************************************************** • 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: • • How to watch math videos • ►5 Tips to Make Math Practice Problems Effective: • 5 Tips To Make Math Practice Problems... • **************************************************** • ►Want some cool math? Check out my Cool Math Series: • • Cool Math Series • **************************************************** • Course Playlists: • ►Calculus I: • Calculus I (Limits, Derivative, Integ... • ►Calculus II: • Older Calculus II (New Playlist For S... • ►Discrete Math: • Discrete Math (Full Course: Sets, Log... • ►Linear Algebra: • Linear Algebra (Full Course) • ***************************************************** • ►Follow me on Twitter: / treforbazett • ***************************************************** • This video was created by Dr. Trefor Bazett, an Assistant Professor, Educator at the University of Cincinnati. • BECOME A MEMBER: • ►Join: / @drtrefor • MATH BOOKS MERCH I LOVE: • ► My Amazon Affiliate Shop: https://www.amazon.com/shop/treforbazett
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