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

[@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.

[@NazaninAshraf-o7c]

Tnahk you for being a very generous to teach us all we need to have the most insight about algebraic abject. and I just need to know a path for studying Matrix calculus, and this will be a huge help to me.

[@JeffAndersonMath]

You are so welcome. If you liked this, check out the comments below where I share links to a lot more videos and content that you might find helpful. Linear Algebra is the love of my mathematical life. Since this subject interests you, maybe you'll enjoy the following: jeffandersonmath.wordpress.com/2022/05/11/more-linear-algebra-please/ Reading your comment makes me want to create a new (or updated) post where I share maybe 50+ books in linear algebra that I love (including many that have great introductions to matrix calculus). For your reference, right now I'm trying to write the best introductory linear algebra textbook ever written. And I want to give this away with no required paywall (I want to fund this with my KZbin and content creation money rather than sell my work to a publishing company). For more about this goal and my current work, check this out: www.appliedlinearalgebra.com/ www.appliedlinearalgebra.com/linear-algebra-laboratory-exercises/linear-algebraic-nodal-analysis www.appliedlinearalgebra.com/blog/for-teachers/linear-algebra-laboratory-exercises/make-eigenvalues-resonate For a sample of my most recent linear algebra writing project, check out the following: kzbin.info/www/bejne/pmW3n6ibn56SbNEfeature=shared That video is incomplete but it's a sneak peak at my larger vision. Along with that video, I'm writing a textbook section so viewers can read and learn in multiple formats. Here is my current draft: www.appliedlinearalgebra.com/s/Anderson_Applied_Linear_Algebra_Introduction_to_Permutations_Draft_v20240613.pdf Thanks for your attention and cheers to your learning.

[@zwakabarakat9317]

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

[@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.

[@aaronTNGDS9]

Great presentation.

[@JeffAndersonMath]

Thanks. I cannot wait for my next releases on KZbin. 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: kzbin.info/www/bejne/aGbamnePbbR8pbM 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 KZbin 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 KZbin 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/

[@EragonShadeslayer]

Wow, super underrated!

[@JeffAndersonMath]

Thanks for your kind words. If you like this video, perhaps you'll like some of my other videos also: www.appliedlinearalgebra.com/s/Math_2B_Playlist_Video_Titles_and_Video_Lengths_Draft_v20240618.pdf www.appliedlinearalgebra.com/s/Anderson_MATLAB_Master_Video_Playlist_Draft4_2023_01_08.pdf I do put a ton of time into my videos and work to make these resources very rich for people who want to build a career using math. One problem (at least when it comes to building my KZbin subscriber count using my previous KZbin work) is that I want to give my students the option to become creators of mathematics. Thus, my videos go into great depth and require commitment from viewers. I don't focus heavily on teaching towards timed tests and I usually push my students to go much deeper than many other college STEM teachers do in their classes. In fact, I like to help students really master concepts with highly intuitive understanding to set a foundation towards applied problem solving. This approach conflicts with the attention economy. Many viewers don't spend enough time really actively watching my videos to get the value hidden withing (and thus I have a much smaller following than other math KZbinrs who do more shallow work). If you want to learn more about my theories of how you can learn math at very high levels, please take a look at the following link: jeffandersonmath.wordpress.com/2023/03/10/how-to-learn-mathematics-at-the-deepest-and-highest-levels/ I will say that I am currently launching a new phase of my KZbin career. In the coming years/decades, I plan to write an excellent Applied Linear Algebra textbook that I provide to the world with no required paywall. For each lesson that I write, I plan to provide typeset lesson notes, high-quality KZbin videos that animate the same content covered in the textbook lesson, full solutions to beginning-level exercises, and much more. For a sneak peak at the next release on this project, check out the following: kzbin.info/www/bejne/pmW3n6ibn56SbNEfeature=shared (this is a rough draft of half of my first of three full-feature videos for my Introduction to permutation lesson). Here is the corresponding typeset lesson notes: www.appliedlinearalgebra.com/s/Anderson_Applied_Linear_Algebra_Introduction_to_Permutations_Draft_v20240613.pdf I'm currently working with a group of students to typeset solutions to the problem sets (that I'll provide for free). To learn more about the larger project, take a look at the following: www.appliedlinearalgebra.com/ jeffandersonmath.wordpress.com/2023/03/08/jeff-andersons-applied-linear-algebra-fundamentals-textbook-project/ www.appliedlinearalgebra.com/linear-algebra-laboratory-exercises Below is the draft table of contents I have created: jeff-anderson-wru2.squarespace.com/s/Jeff_Andersons_Applied_Linear_Algebra_Fundamentals_Table_of_Contents_draft_v20241117.pdf The introduction to Permutation stuff above is a single entry on that 6-page table of contents. If I do the type of work I want, I bet this book is 5000+ pages and becomes the richest introduction to linear algebra on earth, all available at the click of a button with no required paywall. Stay tuned for more developments. This is a passion project of mine that I plan to work on until I'm dead. If you want to see the type of outcomes my students achieve with my labor, check out the following: www.appliedlinearalgebra.com/wall-of-fame Thanks for your attention and cheers to your learning.

[@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.

[@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?