Linear Algebra Final Review (Part 3) || Eigenvalues, Eigenvectors, Eigenspaces & Diagonalization 

I read this comment right before my exam when I was reviewing with these videos, turns out I got a 95% on my final too lol! These videos were super helpful, can't thank him enough.

​@@a23oj28 quick question how was you doing before watching this video?

@@ifeanyiogbennaya7773 I was doing well beforehand, I wasn't surprised with the grade I got on the final exam. On the midterms and assignments I was averaging 98-100%.

@@ifeanyiogbennaya7773 Point being, don't rely on these videos. They are super helpful for review and will shorten the time you spend on it, but you should be consistently doing well the whole semester. Most people are not able to get a 95% just from these videos so the commentor is an exception.

AloneMaru - I’m glad I could help! I definitely get where you’re coming from, as I’ve had similar experiences. I took linear algebra nearly a year ago, and sometimes it felt like we were going into a concept way too fast. I really want you to understand what it is that we are actually finding, so you aren’t just memorizing a computation. Not doing this was my biggest mistake in Linear Algebra.

Wow, that sounds awful. Props to you for powering through, and I’m happy I was able to be a small part of that :)

Navy Dinosaur - No problem! I’m happy you were able to pass. The first half of linear algebra isn’t too bad, but the second half really gave me some trouble. Btw, just saw you subscribed, thanks so much!! Trying to get to 1k in September, so I can actually start making some money aside from Patreon lol. If you know anyone else that could benefit from these videos, I’d appreciate you passing them on!

No problem man. I’m glad I was able to help. How did your final go?!?

good luck on your final, im about to take mine

lies, all lies. - Hahaha I spent so long explaining that.

Anthony Alvarez - No problem!! I’m happy I could help.

Roy Vivat - Thanks so much! I hope RU-vid will eventually start promoting my content lol. We’ll see. Hoping to hit 1k subscribers by the end of summer!

@@LudusYT I'm sure you'll get there quicker than you think. I've already started spreading the word about your channel in my school. I had my linear final exam today and watched all three parts (at two times speed and skipping through a bit) this morning. I think you really helped with the conputational section of the exam.

Roy Vivat - I’m glad to hear it helped, and I appreciate you spreading the word! I hope those time stamps helped you skip to sections that were most relevant. I hope your final went great.

open circuit - Thanks lol.

Sameer Sharma - I think I’m a little confused. Do you mind elaborating on your POV a little bit more? I’ll give you my understanding, and then maybe you can fill in the holes. My understanding is that you want me to either lessen the amount of topics I cover, or you want me to not explain the problems so much and just work through them. My response to that idea would be that when I was making this video, I knew it would be shorter because there was less material being covered than in previous videos. I did a smaller amount of problems, because I thought that it would be sufficient in drawing from all of those Eigen-topics that you mentioned. The way I construct my final reviews is kind of like a survey of the course. I only do one/two key problems per topic, and that way I can conserve time, but also cover the topics enough to where you will most likely know if you are still struggling with that topic. In the case that you are still struggling on a certain topic, my suggestion would be to do more practice problems on your own for that topic. I thought that was fair because these videos all together are somewhere around 3.5 hours long. For classes that I would struggle in, I would study for much more than that, and so I think these final reviews are a good way of being able to judge where you are struggling. That was my thought process, but I definitely want to hear your thoughts, so I can continue to refine my methods. Let me know what you think!

@@LudusYT Well, all I wanted to convey was you solving few problems on the video whilst explaining the concepts with it would make it clearer to a person who does not know anything and kinda just getting along with Linear Algebra. I could follow with you because I know all of this already and you basically gave me even more easier ways to understand the concept and solve problems. But talking for a person who does not know anything and wants to learn through your videos - It will be difficult for them because they dont know the basic ideas. So, I know it takes up a lot of time but you could possibly explain one whole chapter in one video with few examples problems. This will work good for the people who want to learn and be ahead of their peers. I am aware that it is a review session and in most of the review sessions people dont brush up on concepts so cheers to that! That is everything I wanted to convey man^^ Cheers!

Sameer Sharma - I like that idea! Thanks a bunch. What I was planning on doing was releasing a few videos like that, and linking to a full linear algebra course on my website. What I wasn’t sure of, was what to actually put in those videos, even though I had a general idea. I think your idea is perfect for what I want to do. Of course, I have to actually make the course first, and currently I’m working on a Calc 2 course and a Special Relativity course. If you have any other suggestions, I’d be really happy to hear them. Feel free to dm me on Instagram. My at is “learned_tutoring”. Good luck on your final!!

@@LudusYT Thank you very much for accepting the suggestion! I will need those calc courses in winter. So, I guess you're my source haha. And hopefully, you will reach your goals too! Thanks for the info, I will slide into your dms if I have any questions ;p

Sameer Sharma - Sounds good!

Heck yea man! I'm right there with ya. I got a classical mechanics final tomorrow (classical basically expands physics 1 a lot by using lots of calc 1-3) and I'm hoping I can nail a 4.0!

Not sure what canonical form is, but I'll have to look it up. thanks fo the suggestion!

@@LudusYT thanks a lot

I “hate” x1, x2, etc bc it’s different from what most people are used to in high school. In high school we solve systems of equations with x, y, and z. That would be a bit messier if you instead used x1, x2, and x3. For larger problems, it’s easy to see which notation is better (as you noted). However, I didn’t like the change over since it’s easier for me to spot the difference between x and y than with x1 and x2. Ofc, you can’t really write any formulas in linear algebra if you’re not using x1 and x2, you have to be able to represent those larger problems. With that in mind, I understand the switch. I’m quite literally just being salty.