How can you tell if a 2-by-2 matrix is positive definite?

In this video, you learn how to figure out if a 2-by-2 matrix is positive definite. Not only do I provide to you a way to use this by looking at the entries of the matrix, I also show you why this technique works. This quick check can be very useful in the discussion of least-squares problems and also when talking about eigenvalues.

[@zwakabarakat9317]

wow this is actually put really well together I salute you and your hard work.

[@madamus2965]

thank you, it is very helpful especially for beginners

[@JeffAndersonMath]

Thanks for your positive feedback. My goal is to make it easier for new comers to learn these ideas deeply and in meaningful ways. If you like this content, you might enjoy some of my other videos. Here is a list of my current linear algebra videos:
www.appliedlinearalgebra.com/s/Math_2B_Playlist_Video_Titles_and_Video_Lengths_Draft_v20220418.pdf
You might also enjoy my linear algebra course resources:
www.appliedlinearalgebra.com/blog/for-students/welcome-to-math-2b
Here is a list of my Calculus 3 and Introduction to MATLAB videos:
www.appliedlinearalgebra.com/s/Math_1C_with_Anderson_Video_Playlist_Draft0_20190924.pdf
www.appliedlinearalgebra.com/s/Anderson_MATLAB_Master_Video_Playlist_Draft4_2023_01_08.pdf
In the coming years, I will be producing much higher quality videos (think 3blue1brown style but with a written textbook included). Keep your eyes pealed for some very special content.

[@zwakabarakat9317]

awesome, clear and beautifully made video, thank you and have a wonderful day.

[@JeffAndersonMath]

Thank you for your kind words and feedback.
If you like this video, you might enjoy some of the other ones I have available for linear algebra:
www.appliedlinearalgebra.com/s/Math_2B_Playlist_Video_Titles_and_Video_Lengths_Draft_v20220418.pdf
or for learning how to code in MATLAB:
www.appliedlinearalgebra.com/s/Anderson_MATLAB_Master_Video_Playlist_Draft4_2023_01_08.pdf
You can also find some good learning resources for my linear algebra class on my course homepage:
www.appliedlinearalgebra.com/blog/for-students/welcome-to-math-2b
In the coming months and years, I'll be producing videos that come along with well-written textbook sections to support deeper learning from the video. Keep your eyes posted for more on that.
Thanks again for your attention and cheers to your learning.

[@yooozhang5239]

Sure helpful and clear. I like the way you use a separate paper to show the definition, and show it each time you recall it in the process of prove. Thanks

[@JeffAndersonMath]

You are most welcome. I'm happy my work helps you learn. Keep up the hard work. I know you can learn anything you want to.

[@aaronTNGDS9]

Great presentation.

[@JeffAndersonMath]

Thanks. I cannot wait for my next releases on RUclips. I plan to produce much higher quality graphics and also include a full drafted textbook section with each release.
For a sneak peak of the work, check out one of my more recent uploads:
ruclips.net/video/25wiDY8OIoQ/видео.html
That was a test of new video production skills I'm building. That video is one of a series of three to translate content about permutations into high-quality RUclips videos. Below is a link to the draft content for this upcoming video series:
jeff-anderson-wru2.squarespace.com/s/Anderson_Applied_Linear_Algebra_Introduction_to_Permutations_20240309.pdf
This is part of a much larger textbook project.
In addition to being freely available online, this textbook will also feature high-quality RUclips videos (like 3blue1brown). Here is my current draft of the table of contents for my work:
jeff-anderson-wru2.squarespace.com/s/Jeff_Andersons_Applied_Linear_Algebra_Fundamentals_Table_of_Contents_draft_v20240227.pdf
Here is a brief description of the larger project:
jeffandersonmath.wordpress.com/2023/03/08/jeff-andersons-applied-linear-algebra-fundamentals-textbook-project/
I am working to produce full solutions to the corresponding beginner-level questions so that interested viewers/readers can check their work.
Thanks for the kind note and cheers to your learning.
PS. If you like learning about linear algebra, you might enjoy some of the resources I highlight int eh following blog post:
jeffandersonmath.wordpress.com/2022/05/11/more-linear-algebra-please/

[@Jetstreamer0]

This is excellent! Thank you!

[@JeffAndersonMath]

You are most welcome. Thanks for your positive feedback... Stay tuned for many more videos in the coming months and years.

[@financebeat9578]

thanks for the class

[@JeffAndersonMath]

You are most welcome. Thank you for your feedback. I do wonder:
What did you find helpful? What do you wish you could find more of?