Thank you to everyone who pointed out the typo at 6:53, where the component-wise sum should of course be [x1+x2, y1+y2]. In general, little mistakes in videos like this will be mentioned in the video description.
Curses! I thought this was finally the answer to the dissonance I feel dealing with vector spaces coming from data analysis. [Yes, despite the row/column operational equivalence, the baseline pedagogy is *slightly* confusing] Not that anyone really wants that mess of crazy to make more sense,...and I have to reformulate that more cohesively before I even try. But for that brief moment, I thought the nonsense in my head actually had a cause! Eh...maybe someday you all can bask in the bedlam that is abstract analaytics.
@@honest_bishop5905 A lot of RU-vidrs like to have a say in who advertises on their videos. I just commented in case Grant wasn't aware and would want to change it. Not assuming that's the case, just sharing information.
This is really hard for me. I cannot tell you how long it took me to just understand this. In 1 lecture I have 8 pages of notes and answered questions. I'm 13 and wanna be a Machine Learner Engineer. I'm doing this for a better future, but for some reason school makes it just harder. Hope in Highschool I can get college credits, I need help haha. Can someone please tell me what Linear Algebra Vector would fall under for Engineering? Computer Science or Mathematics?
Please delete this comment. I'm serious. It's against Google Adsense policies to have your users click on ads to increase revenue. No, this is no joke, I know somebody whose Adsense account was suspended because of this.
@@MBTIMemes well he's not clicking ads, he's just watching them. and he is watching them because it's his choice, not because the creator of the video told him to.
Well I know the video has 6 years already and one comment won't make any difference, but man... What a great job you did. It's one of the most emblematic experiences of what RU-vid did with learning in our times. Incredible work!
@@iridium8562 Yeah man... so easy to complicate things right? but to simplify complex things... oh boy... not for everyone. Became a huge fan of the channel
I had given private math lessons to high school students when I was an undergraduate student in mechanical engineering department with an idealist promise to myself stating that I will prove all the formulas to the children which I was forced to swallow in high school.After 24 years seeing a person who has the same targets made me feel that we people around the world with the same mind set up against math , physics are not alone. I am deeply gratefull to watch such a series for linear algebra videos.Hats off
@@abdulmeliksaylan3292 konuyu anlamadığın sürece sınavın önemi yok bilimsel açıdan bakarsak. konuyu anladığı sürece sınavda da yapar çocuk, formülü de öğrenir.
I've always wanted a more intuitive understanding of material like this, and all it takes is the right teacher to make the lightbulb go off. This guy has not only developed a strong intuitive grasp of the subject, but is then able to seamlessly transfer that information verbally with engaging visuals. All too often I've listened to people who "know" things, but struggle to explain with coherence. The world needs more teachers like this guy.
Often, I understand something and can't explain it clearly to somebody else. I envy 3Blue1Brown for having the ability to convey this information wonderfully and create such excellent graphics.
Brilliant! I came here as a Unity game programmer to get my 'head round' using vector maths to controll a game character, in three dimensions, to approach a waypoint. Already things are a lot clearer and less headbanging will be necessary - the explanation is done with such clarity I am enjoying learning, even more than playing video games. Thank you for taking the time to do this. Peace
😅😢😢😢Leviticus 18:22 KJV Thou shalt not lie with mankind, as with womankind: it is abomination. Ephesians 6:10-18 says, Finally, my brethren, be strong in the Lord, and in the power of his might. Put on the whole armour of God, that ye may be able to stand against the wiles of the devil. For we wrestle not against flesh and blood, but against principalities, against powers, against the rulers of the darkness of this world, against spiritual wickedness in high places. Wherefore take unto you the whole armour of God, that ye may be able to withstand in the evil day, and having done all, to stand. Stand therefore, having your loins girt about with truth, and having on the breastplate of righteousness; and your feet shod with the preparation of the gospel of peace; above all, taking the shield of faith, wherewith ye shall be able to quench all the fiery darts of the wicked. And take the helmet of salvation, and the sword of the Spirit, which is the word of God: praying always with all prayer and supplication in the Spirit, and watching thereunto with all perseverance and supplication for all saints. The bible is no old book. You have to really let Christ open your eyes; to see the world in shambles. Many people say it's a religion to lock up people in chains, and say it's a rule book.. why? Because people hate hearing the truth, it hurts their flesh, it's hurts their pride, it's exposes on what things have they done..people love this world so much, s*x, money, power, women, supercars.. things of this world. Still trying to find something that can fill that emptiness in your heart. You can't find that in this world.. only in Christ, the bible is no chains, it's a chainbreaker. Breaking your sins into pieces... Repent now, and turn back to the true Lord only.. God bless. 😢😢😢
If there's anyone like me with virtually zero prior knowledge in linear algebra and feeling like an idiot not understanding what this series (particularly the later videos) is about and why many others are praising Grant, I suggest you pick up an elementary linear algebra book to understand the fundamental concepts before continuing on. This lecture series focuses on the intuitive side of linear algebra, but I personally found it hard to gain intuition when I didn't know what LA tries to solve in the first place. After you've gone through the more formal basics, things will start to click. About two months ago, I watched the entire series of lectures understanding only abut 30% of it, now I'm back and this series is supplementing my knowledge very nicely. I hope this helps anyone that feels the same way I once did.
Yay! You helped me. I am waiting to take Calculus, I just switched my major to Plant Science. I don't remember a thing about Algebra even. I will double back understand elementary, then come back!
@@Anaghish I mostly used two books, 'No Bullshit Guide to Linear Algebra' and 'Elementary Linear Algebra by Howard Anton', plus a few other online tutorials and guides on solving linear algebra equations using python. There are lots of resources on the web (many are even completely free of charge), so it should not be too difficult for you to find books or courses that suit your preference and level of knowledge. :)
I've been taking Calculus III for weeks, and I still didn''t understand the simple intuition behind these vector facts, yet. Yet, in this video I understood it all, instantly. Thank you, Grant! You're one of the best!
I sat in my first Calc 3 class yesterday and he jumped straight into vectors as if we all took linear algebra... this vid made everything come together though
0:00 Intro quote 0:20 three distinct ideas about vectors 1:57 specific thought to keep in mind 2:41 the coordinate system 4:36 vector addition 6:54 multiplication by numbers 8:10 overview of the topic of the series
Grant, I'm a physicist professor and, in Brazil at least, the high school maths don't teach about vectors, and the physic way to teach is... well... is physics. Since 2018 when i first saw this vídeo I give at least one class about vectors to the students, so I really want to thank you ♥
I am Brazilian, went to public school, and I learned about vectors in my last year of middle school and during high school as well. I guess it depends on what region/state you live in Brazil.
@@manawa3832 You can have too much democracy which creates referendums about everything. And then emotions only will win the vote because everybody thinks he or she is an expert because his or her emotion is correct about the issue. Too much democracy = distopian world. A great modern example of this is the UK referendum for leaving the EU. It's all based on lies and deception. Facts don't matter anymore in full fledged referendums. It's all about hate and emotions.
@@douwehuysmans5959Mindfulness used to be called pseudoscience, but with the advent of neuroscientists analyzing monks' brains scans and the research on its decrease of blood pressure by biologists and relaxation from psychologists, it's pretty much considered science now. Sometimes pseudoscience yesterday is science today, such as how people thought that the sun used to around the Earth before.
The way you explain everything is so easy to understand. You start off assuming I don't know anything, and slowly build up to more complex topics, all within the timespan of 10 minutes. It's so easy and approachable, even for someone (like me) who hasn't even learned the basis that this is build on. Your teaching style is really great. Keep up the good work
About to watch this series all over again, having just finished it and it's safe to say that these videos are the best thing that could have happened to me in my linear algebra journey. Literally connected all the dots!
Crisp..Clear and Sharp. The way you teach is awesome and also the your audio, teaching and the aniimation...all go in perfec rhythm. Thanks for the video.
Wow! I was a high school physics teacher for 32 years and I never knew why scalar quantities were called “scalars” until 7:57 in this video. This made my day!
I have to say that this series fundamentally destroys my knowledge of vectors, and after finishing it, builds the concept up once again, but this time more elegantly. Thx Bro, u helped me a lot.
I can't imagine how I loved this way of expressing math conceptual information. This project explore in a rich way the connections between math and other knowledge areas. Thanks a lot for bringing it for free for students and even for teachers all around the world. I'm a Brazilian physics high school teacher and expect to use your material, and of course, promoting your work with my students!
This is probably the best and most straightforward, thorough, and honest explanation on the topic I've found. I love people who say, "This is just a fancy way of saying X." Aside from being clear to understand, it's also just a really wonderful character trait. This guy nails the intuitive explanation.
Dude, this is really good. I think the visuals are the key. It's really hard to comprehend linear algebra without heavy use of graphical tools. And this video has a ton of visuals. Made it easy.
Agree. Studying the abstract material without heavy emphasis on the visual understanding devoid you of really understanding what are you really studying
Sir, your videos are terrific, especially this series along with the calculus series. I always do very well in my math courses, but I am rarely satisfied with just getting the computations right-I seek an understanding of the math that extends beyond the numbers and an understanding of how the math applies in the real world. It usually takes time to answer all of these questions on my own, but your videos clarify so much and extends my interest, so thanks. p.s. It would be great if you did series like this on other courses, like multivariable and DE.
The multivariable calculus course on Khan Academy is by him (an early work, not as polished as this one, but still pretty good). www.khanacademy.org/math/multivariable-calculus/thinking-about-multivariable-function
Dude you just saved me. I'm a student in his last year, and I want to get a deeplearning job. I'm also doing my diploma project in 3d object detection. I forgot everything from the first year, when I had linear algebra and calculus, so your two playlists about those subjects are a blessing
I am immensly grateful for this channel for opening my eyes to the underlying ideas behind these mathematical concepts. Earlier I used to solve problems related to vector algebra mindlessly without actually appreciating the beauty of it all. Now I feel very enlightened. Thank you so much!!! Your channel is indeed a noble pursuit.
Coming back years after having watched these videos to thank you. In the past they gave me great intuition about linear algebra (a topic which I didn't know before checking these videos). Recently, the idea of looking at linearity as the line preserving property helped me look at a problem with a diferent angle which allowed me to solve it. thank you very much!
I actually can not thank you enough for making this course. I was struggling with my professor to learn something that I know I should understand. I then went to another youtube playlist, which was great, but was only the computational side. This series explaining what the math is actually doing and how it works is absolutely what I was looking for. I seriously can not thank you enough for making this. I finally understand what is happening and the math makes so much more sense now! Plus the cherry on top is that all of this was free.
Following this playlist along with a theoretical lecture series is just awesome . Getting intuitions and also the required theoretical knowledge is amazing.
I want to congratulate you. The way you explained vector addition as "steps" is absolutely excelent. I've had a Linear Algebra course recently and I was always confused with the visualization of the result of vector addition. But thanks to that beautifully illustrated explanation, it was some sort of "eureka" to my brain. Fantastic job!
Thank you 3 Blue One Brown I’ve been out of school 6 years and I’m starting calculus this coming semester. I was incredibly stressed that I wouldn’t be able to keep up with people fresh out of high school, but your videos helped me remember why math can actually be enjoyable and that mindset has helped me a lot while studying.
I love this channel. I feel like such an idiot all the time in math class because I don't understand it and the teacher says I should know this thing or whatever, but then I try to catch up and this breaks it down in such a way I can visualize EXACLTY what's happening and then put that on paper into the proper equations.
I think this is my first video of yours I've watched and I can already tell I'm going to love your channel. I'm somehow excited to learn linear algebra now, something I could have never imagined saying!
Literally can't thank you enough for making these videos. I would have failed my class and subsequently failed out of college without the understanding these vids helped me get. You're doing good work here
When I was in school struggling to make sense of this and I couldn't, my questions annoyed my classmates. "WHY CAN'T YOU JUST FOLLOW THE FORMULAS? " I wish I found this at that time
Usually i don't comment videos but man... I'm a Software Engineer student who is trying to get into the Machine Learning field. I won't lie, it's scary because i think i lack so much the math skills necessary to fully grasp the concepts, but, I decided that it's crucial to follow my passion. I recently discovered your channel, and i have to say... your math passion is contagious. The way you beautifully present the concepts, the elegance of the animation, the way you make complex topics look so simple is just mindblowing. You're following your passion and that is reflected on your outstanding work. Thank you for giving me motivation to follow mine, and for teaching me like no one teached me before.
Just completed my Introduction to Linear Algebra course with full marks for the final exam. I remember I had a slow start in the course, and a lot of things didn't click until your elegant and highly visual explanations helped lay the groundwork for a deeper level of understanding. Came here to say thank you for all the work that you're doing, the world is a better place with you and all your resources!
in my mind I sometimes imagine myself explaining a subject perfectly, and in practice I always fall short. Your videos are what I picture a masterful presentation to look like...I wonder if my missing piece is mastery of the editing tool you are using because you seem able to put your thoughts into edited content
From a 60-year old who almost failed maths at school as a teenager because it was SO BORING, a thousand thanks for this engaging, accessible, warm-hearted, beautifully-made tutorial. With best wishes from Cape Town!
I majored in math in college. I relied on my math degree for other careers, flying and law, in varying capacities. I'm now considering a new career in teaching. I can say that you are the best math teacher I have ever encountered. So, fwiw, I really appreciate your refresher courses (to me) as I consider changing careers one more time.
Are you the best teacher alive? my heart is pumping joy for this video series; I can't organize properly a huge array of words to thank you for this knowledge: accurate, genius, empathic, pleasant, understandable, magical, logical, expressible, beautiful, knowledgeful, precise, clever and many more. PS; I made some words...
This makes way more sense then what I was taught in class: “here are some numbers, do this this and this to find this kind of answer...blah blah blah.” I wasn’t even taught what the determinate really represents, just to press the button on the calculator.
I wish if such learning experiences were available during 90’s. Learning and easy access to information and such courses is a blessing for this generation.
Could you possibly make a course on the essence of probability, chance and statistics as well? Thanks so much for your work! Love your style and videos!
Really I was taught all this stuffs in University without even knowing what they are and where they are used . That's why I hate education system , School and Colleges are only for Degree , if u have to make your future bright then you'll have to learn all that from outside. Thank you so much @3Blue1Brown you are really helping me a lot. You owe my respect , you deserve much more 😇
I don't know, I'm now 70 and decided to learn Machine Learning as hobby. I'm very thankful to our high school where 55 years ago I learned the basics of vectors, If I would have to start from the scratch, I don't know where I could start today. With the basic knowledge I got in the past, now a simple RU-vid clip can help me to understand and move quickly to the next level.
If u are going to college thinking u dont need an extensive research of ur own. You're doing it wrong. Professor are researcher, sometime they are too far ahead that they dont know how far behind the students are. U are expected to research more about what u still not understand tho😅 so many college graduates feel like they didnt learn anything becuz they took college like highschool class.
I've always thought vectors and scalars were so different that we couldn't use them together. Then I stumbled upon Professor G. Strangs' Introduction to Linear Algebra and was stuck on how to picture this "other" world full of vectors, arrays, matrices in graphs, when all I've learned was Calculus. Then I watch this video, and the quote "The introduction of numbers as coordinates is an act of violence" really threw me away. I learned so much just from this video alone, and can't wait for more! Thanks!
Wow. Incredible videos, thanks for making them! I can never remember things unless I have the geometric understanding too. Math also become a lot more meaningful when you understand the geometry behind it as well, instead of just memorizing a list of steps.
I found these videos while frantically trying to cram and understand all the concepts for my second linear algebra exam. I'm pretty sure I bombed that test, but here I am, back here watching these videos starting from the beginning. You give such great intuition, and hopefully by the final I'll have a visual understanding of all the concepts rather than just trying to memorize a list of steps to reach an answer that has no meaning to me. Just hours before my exam I didn't even really understand what the determinant was or why the determinant being 0 meant linear dependency until I watched one of your videos on it. Thanks for this amazing playlist!
I'm really impressed by here --> 5:58 I just watched only one video in this linear algebra course, but I already understand essential about 'Why did the concept of vector arise'. When I was highschool, I don't understand the context of vector. So even though I get a good score in geometry subject(It's a korean math curriculum which include vector. I'm the one of korean viewer in this channel), I feel not good. but now I really get it. thank you so much😁
