I very much doubt you'll ever read this, Professor Pavel, but in case it does happen: I hope that one day I'll get to contribute to society by teaching as thoughtfully and diligently as you do. Many a time I see colleagues, as I do myself, feeling stupid and becoming insecure or even developing anxiety and depression simply because most professors don't impart knowledge but rather mere procedures to solve exercises. Much respect, from a brazilian fan. :)
Prof. Pavel, Thank you so much for this video. I'm an aspiring mathematician and studying to become a math teacher. I am currently a peer educator for Chaffey College in California and I work at a local tutoring place. My goal is to become a math professor! However, I have several learning disabilities that make it hard for me to understand textbooks. It's been a while since I've heard a mathematical concept explained so succintly and clearly. It brought me such joy to be able to understand this concept and be able to explain it to someone else. Upon watching this video, I pulled my husband aside to watch this video in sheer excitement! It was so easy to understand for him, as well! Thank you for bringing a smile and knowledge to me. I can't wait to use the techniques here! I hope I can leave even a portion of the impact you leave on the world every day on my current and future students! Sincerely, A.M. Vega
This linear algebra course is a joy to watch... I wish I had a professor like you when I studied this subject for the first time ... I'm starting to love linear algebra 😀 thank you 🙂🙏
This is my first video that I tuned into on your series to gather further insight into A=LU. This is really good. I love your side commentary that adds perspective. I will be watching your videos to understand linear algebra going forward (BTW 3blue1brown has greatly helped me get my linear algebra "thinking hat" on, but I need to now fill in the details.).
wow! i had previously watched a video on LU decomposition but they only gave the process and not the explanation. dissatisfied i had come to your channel.now i think i understand it well.thank you sir
I don't see how [1 0 0 ; -4 1 0 ; -7 0 1] is an elementary matrix. Isn't an elementary matrix one that which can be obtained by a single elementary row operation on the identity matrix? I think the matrix above requires two operations (even though it can be applied at the same time).
If I have to write a program for LU decomposition I wouldn't use product of inverses to get matrix L Each iteration of gaussian elimination gives us zeroes in the column below diagonal so we can insert there multipliers used for elimination and skip this and previous columns in elimination I would introduce an auxiliary vector to record row interchanges
How does switching the location of pivot on the matrix (ie switching rows) improve numerical stability? In this example how would we switch the rows of A without performing the first step of GJ elimination?
I didn't explain this in the video, but I think that you will find an example of things going wrong numerically in the following link: math.stackexchange.com/questions/1143471/gauss-jordan-elimation-unstable
The way he presented it is not so useful for writing a program in languages like Pascal or C Even for pencil and paper calculation it is easier and quicker to do gaussian elimination with record of multipliers
long shot.. but still hoping to get an answer. I asked the following question on math exchange math.stackexchange.com/questions/3605451/checking-is-a-point-lies-inside-the-area-enclosed-by-multiple-equations-using-li . can you help?
this guy is amazing at what he does but hes extra some of us are just engineering students and we're concerned with the procedure but aside from that good work
It is societies tendency of labeling and putting stereotypes , that an engineer is a particular type of person that is the human beings down fall ,don't look at my preferences and think you can sum me up with just a comment you can not begin to fathom the depths of me.
