Vectors | Chapter 1, Essence of linear algebra

[@3blue1brown]

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.

[@elijahfromm7108]

FYI your video has Trump ads

[@darthkenobi66]

could you make videos about tensor?

[@jpnesseth]

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]

@@elijahfromm7108 so?

[@elijahfromm7108]

@@honest_bishop5905 A lot of KZbinrs 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.

[@ryanshugart8539]

literally watching all of the ads possible to give this man as much revenue as I can because he deserves it

[@EricDannerW]

I think he has a patrion too(if you have an extra 5 bucks)

[@ConsumerOfCringe]

i think he also doesnt monetise his vids

[@gustavom8726]

better if you donate

[@MBTIMemes]

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.

[@antimartyr09]

@@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.

[@DarkCebolix]

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 KZbin did with learning in our times. Incredible work!

[@ganalord]

It's an life changing work

[@Wanderibbon]

Extremely useful :)

[@iridium8562]

this has got me through 2 years of pre-engineering school, even tho i study in france

[@DarkCebolix]

@@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

[@originalveghead]

What @DarkCebolix said. Thank you.

[@michaeltheisen]

I watch this playlist whenever I want to feel happier. There is a sense of peace I achieve in the beauty, perfection, and simplicity of mathematics.

[@Ash-bc8vw]

Same

[@dlrsnate5100]

Watching this only ever having made it to algebra thinking I can ace the course Lmao

[@joesmith5970]

cringe..

[@Th3-ch0s3n0n3]

@@joesmith5970 tnx for commenting, this beauty deserves all the engagement it can get!

[@joesmith5970]

@@Th3-ch0s3n0n3 no worries! This channel is great and I'm happy to support it.

[@h.cihankurtulus3070]

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

[@moonprint7547]

We need more teachers like you sir

[@abdulmeliksaylan3292]

kesinlikle hocam ama sınavlar kanıt yapabilenden ziyade ne yaparsa yapsın hızlı yapabileni sever

[@ikinoktace1280]

​@@abdulmeliksaylan3292 konuyu anlamadığın sürece sınavın önemi yok bilimsel açıdan bakarsak. konuyu anladığı sürece sınavda da yapar çocuk, formülü de öğrenir.

[@ayi_oglu_ayi]

@@abdulmeliksaylan3292 hızlanmanın temeli de zaten konuyu anlamaktan geçiyor, bu sabah calculus sınavından çıktım ve konuyu anlamasaydım asla zihnimde grafiklerin vs canlanıp cozume giden yolları görebileceğimi sanmıyorum. Tabii bir çok konuda aynı örnek verilebilir

[@bramblewoodhall4757]

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

[@vedantzz]

Same 😭

[@TabooRetka701]

Good luck in your path in programming and game development!

[@salthal]

Good luck!!

[@PraiseTheLordyourGodJesus]

😅😢😢😢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. 😢😢😢

[@matt2.019]

god, learning math is so much more enjoyable when I'm not in school

[@keylevelfx2964]

Right! I "hated" math at school, but now as an adult, I found that I actually love it and I think the learning environment plays a big part in that.

[@joycesimbulan186]

I totally agree!

[@apolo7075]

X2 :v

[@matthewdelay2797]

I'm currently in school and only like learning math when it's not in class😂

School is just a nursery designed to take away your most valuable years and making you lose time until you're 18.

[@miketant3509]

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.

[@antidotejack2771]

I feel the same for this gentleman.

[@chasebeams]

This sounds like a canvas discussion post

[@paulojo720]

He is one of the best

[@thomasisernhagen8263]

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.

[@baconheadhair6938]

@@thomasisernhagen8263Do you understand it then or have you just memorized a process

[@valarikjeffeerson7226]

Physicits: *uses vector and linear algebra to describe motion of a body" Mathematicians: Everyday we stray further away from the origin.

[@stumphole145]

LMAO SO ACCURATE

[@mathlover2299]

As the great Richard Feynman said “Physics is to math what sex is to masturbation.”

[@plutoniumisotope205]

@@mathlover2299 application???

[@mathlover2299]

@@plutoniumisotope205 Real life?

[@plutoniumisotope205]

@@mathlover2299 no is he describing physics as a application of math

[@mobyj4794]

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.

[@cynthiab9999]

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!

[@pragati9821]

No it's not that great it's just average..,...these are basics only

[@Anaghish]

Can you recommend some books for beginners?

[@mobyj4794]

​@@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. :)

[@ehtishamhassan8146]

Thanks.

[@olaoluwaolaniyi2241]

I never imagined I would understand scalars and vectors this clearly in just 8 minutes. Thank you!

[@atfti]

I know right?? I feel my neurons changing patterns because of this video

[@kjekelle96]

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

[@justamanofculture12]

Let me thank you on the behalf of everyone.

[@kjekelle96]

@@justamanofculture12 You're welcome ;)

[@weirdguy320]

what about unit of vector ? like in physics we have unit also with magnitude

[@gameboyv1790]

Thanks

[@ysnsmth]

thx

[@Vocalo_fan]

This was recommended to me by my algebra teacher and although his classes are very understandable You are truly a lifesaver Yes, even in 2024 people watch your videos, and I am so grateful, genuinely, that you made these lessons, they are going to make life so much easier

[@ryzk_muzik4949]

Bro's got really good teacher who also suggests really good things 😭😭💀💀

[@tanusszabo]

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 ♥

[@ovelhanerd1768]

Bom saber que existem bons professores como você!

[@johndalton4559]

damnnn...kids out nhere having vectors at age 14 while others dont have it in all of highschool dafuq

[@89ccmf]

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.

[@aubreeswart2206]

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!

[@flowmotion_2]

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

[@dreamydailine]

Wait what Is this college stuff?

[@scienceium5233]

Me too

[@HenryTechBoy]

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!

[@writethatdown100]

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

[@zhyakoxalid6892]

Yes he is

[@aftereffects713]

I am having tears in my eyes. The concepts that confused me for years are this simple. Thank you.

[@kavinbharathi]

I represent the cursed group of people who were not taught that vectors can be represented as matrices...

[@bradvincent2586]

yeah this is blowing my mind. Literally had no idea, and I got mostly A's working up to calc 3. That's what you get with government run schools

[@kavinbharathi]

@@bradvincent2586 Actually I am from India and even the most appreciated schools don't teach that idea...

[@irfanjames]

@@kavinbharathi Same here in Pakistan. But curiosity to watch these kinda things is what our students need.

[@kavinbharathi]

@@irfanjames True : )

[@kavinbharathi]

@Gaurav verma I agree

[@bradydyson65]

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.

[@林均頤]

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.

[@laquzoeshiyasha]

this. this is what is needed to be done with the half-assed concepts which the education system vomits on the students.

[@lucasdossantosalthoff2790]

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!

[@ryanpark7905]

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😁

[@bashhau]

It is just crazy how the most overlooked subject in computer science throughout my school time turns out to be the most influential and relevant today. Thank you @3blue1brown

[@GoldenRockefeller]

Rotating in 3d at 4:20 was a nice touch. Thanks for that.

[@mesplin3]

agree

[@deepakkumar99933]

liking this cuz 4:20

[@NoemeMatos77]

Nice observation!

[@elon.2193]

i thought all pakistanis thought of was bombing people @imran

[@user-tm1ix7xi1n]

imran876339 So, should we assume every middle Eastern are terrorist?

[@Fr0doG1]

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

[@anonymouse8616]

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.

[@akzork]

Did he just say he creates these animations through code?

[@danielwhiteside3610]

Yep. I think he has his python animation library available on GitHub

[@wanderer7480]

Yeah, he uses the library he wrote himself for the animations. It's name is Manim and it is open source.

[@badreddine341]

@@wanderer7480 that's quiet fabulous to say the least

[@cozz124]

yeah hes crazy and i love it

[@krox477]

This is one of best explanations ever on vector math

[@japonjapon6242]

who you are?

[@ChameeraDedduwage]

If more people watched these, we'd have less pseudoscience and more progress. Hands down, one of the best. Kudos.

[@manawa3832]

Yeah like believing democracy is good

[@HermanWillems]

@@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.

[@manawa3832]

@@HermanWillems Yeah democracy tends towards populism as much as authoritarianism tends towards elitism

[@douwehuysmans5959]

Not all pseudoscience is completely worthless. Think about mindfulness and meditation and stuff like that.

[@ravenn2631]

@@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.

[@anusha8085]

8:52 - 8:56 what a visual treat. This series is so amazing.

[@sarahduncan1226]

This is absolutely lovely and wonderful, with one small caveat. The explanations are just beautiful and so crystal clear. The caveat is that as a woman in tech I wish that at 1:47 you'd said "we'll ignore her for now" or "this" or "it", something other than "we'll ignore him for now," where him refers to a mathematician. I realize it's a really small thing, but for me, it's one cut in death by 1000 cuts. I get the message over and over again, day in and day out, that technical people are "guys". IT guys, storage guys, scripting guys, and mathematicians are always "him." I realize that the male is meant to represent male and female, but I know that even I generally picture a man when I think mathematician, physicist, astronomer, IT guy, etc. So I hope in future videos you might consider using she for your generic tech person, or a neutral pronoun. Thank you so much for your beautiful work!

[@Gracken420]

facepalmed for not realizing 'scalar' referred to scaling

[@Peter-bg1ku]

Would be more intuitive if it was "scaler" instead of scalar

[@nicedreams6010]

You are not alone my friend.

[@AlchemistOfNirnroot]

@@Peter-bg1ku Phonetically identical though.

[@dima__b]

Mind blown🤯. It was even harder to realize since English is not my native language

[@lolicanadian]

Yeah, I didn't really notice that either until second-year physics, which is weird because I also take CS and mathematics.

[@Treebeard1671]

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!

[@amateur1004]

Same 😅

[@lodgechant]

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!

[@Chadderbox]

This is incredible. It took my teacher 2 weeks to stumble over this and you nailed it in 10 minutes.

[@nikhilparmar9]

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.

[@angelpenarolo7408]

I just had a really interesting experience, it’s kind of unrelated, but interesting nonetheless. I know nothing about linear algebra. And after watching this video, I feel like I know everything about linear algebra. I felt what it was like being on that first peak of the dunning Krueger effect, which was fascinating. Though I just learned the basics, I felt like an expert. I had to remind myself that this is just the beginning. Then, when he said what he’s going to talk about in the next video, it was like going past the dunning Krueger “peak”, by realising that I don’t know that. Can’t wait to learn more 3b1b is an incredible teacher.

[@lanceang795]

I’m a programmer using OpenGL and am understanding matrices more and more in this series. Thanks 🙏!

[@jadduajones]

I really love how you didn't restrict the lesson to the euclidean metric! Cheers!

[@KI4ASK]

Outstanding. Love the clarity between physics, CS, and math approach to vectors. Makes sense.

[@thomasshaw6169]

This has to be my favorite math channel.

[@chuksjr.1440]

It definitely is!

[@frontstudent9858]

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.

[@ateampossible]

Agree. Studying the abstract material without heavy emphasis on the visual understanding devoid you of really understanding what are you really studying

[@zhancao7909]

Thanks!

[@yyeeeyyyey8802]

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!

[@dreadfullyd1701]

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!

[@cml64_]

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!

[@twinbladevolt8679]

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.

[@phantomproduction5757]

This playlist is among the best things humans have created🙏.

[@WiredWizardsRealm-et5pp]

Every time I sacredly click the video thinking oh! this video might go above my head and everytime it seems as if I was scared for nothing..! He is setting up the standard to not miss any subject which can't be explained best possible way in the first try.

[@SashaTownsendTulsa]

Even though we use slightly different notation for vectors in Calc III, I’ll be sharing this with my summer school students. Thank you, Grant!

[@sidowachholz5133]

Huu

[@sidowachholz5133]

Jjiijnn

[@ppppp524]

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

[@ServantotLY]

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!

[@juanmanuelsierra1485]

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.

[@qaziyahya8472]

How is it going? Did you get into ML?

[@arthurgoldblatt5822]

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.

[@83vbond]

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

[@affanahmedali187]

I have taught linear algebra and vectors or so I thought until I came across your series. You sir are the EPITOME OF JOY!

[@ManasMittal-pl6vg]

Following this playlist along with a theoretical lecture series is just awesome . Getting intuitions and also the required theoretical knowledge is amazing.

[@MMABeijing]

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

[@KRYoung_dev]

Thank you so much. I got into a sort of ML bootcamp, where I suddenly find that ML is just math with a fancy coat of paint on top. Well, I majored in art and psychology, got a D in calculus 14 years ago, and never even took linear algebra. So my anemic math skills are hampering me in an extremely fast-paced program where it's like they are speaking a different language every time somebody busts out the Greek letters. Looking up these essential mathematical concepts mostly just brings up *how* to solve test problems and complete homework, whereas for ML you need to understand *why* these methods work. Thanks to your videos, I can get up to speed in minutes instead of months. I'm really, really grateful!

[@professorx6328]

I love this guy! I'm considering going into CS and his take on the CS views of linear algebra is amazing!

[@Horsesdontbarf]

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.

[@Christian-Peter]

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.

[@steven21736]

What sort of law did you practice?

[@Jamieeee-ht7qk]

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.

[@caspermcgonagle1532]

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.

[@AmitSingh-sf5qp]

You worth 100 times more better than the institute of India who charge $2,500 for 1 year course to teach these topics . And clearly this is the reason why foreign scientist are doing better than Indians . Indian education system is focused on competition only they don't teach the values of concept like you . And this is the first time I have ever seen crystal clear video on any topic that's why I watched is thrice (some part ). At last , i want to make a promise to pay you for this video . But after between min 6 max 10 years from today .

[@humans3009]

As an Indian i can totally relate to what you said and it's extremely depressing😭

[@rodneiatanki]

mistake on 6:52. shouldn't it be x1+X2 and y1+y2 rather than x1+y1 and x2+y2?

[@rodneiatanki]

and I love your videos!

[@Dani0x1B]

Yep, it should.

[@TacoSt8]

Lucas Dias i was really freaking out thanks!! also i havent take any lessons of this!!

[@WordMapsOrg]

Agreed, but it was corrected incorredly v instead for y

[@viktorneshikj6056]

only true mathematicians such as us spot mistakes :)

[@memoahmed156]

just Wooow, I am a CS self-study learner and I was struggling to understand how on earth there is more than a 3rd dimension in a cube ( Business Intelligence people will relate) and it turned out that 1st, 2nd and 3rd dimensions applies on physics not CS, I am so thankful to you

[@nicholascunningham6936]

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!

[@umariktokyo]

Only in places like this, you understand the value of the internet, and beauty of math. Thank you for everything!

[@RAUSHANKUMAR-w8q5u]

I have never seen more visually attractive lecture on vectors than this one. God protects you .

[@candidatesvoice8826]

Your teachings are more than Bad Ass!!!! It is simplistic yet complex. Its beautiful.

[@Yasharvl]

this is exactly how I feel about these channel: An in depth and elegantly put together mixture of different mathematics subject, clearly explained.

[@duckymomo7935]

Nice, simple and clear but definitely not complex...(these topics can get very advanced fast)

[@13RedCorpse]

I never thought I could be so excited about linear algebra as I am now (thanks to these videos).

[@VisualMaths0]

kzbin.info/door/vkJke43iz5UyhFPZzgMt3g?view_as=subscriber

[@Felipe-53]

This man should be given a nobel prize for such terrific teaching. Thank you so much for producing high quality content for free!

[@InGodWeTrust-4ver]

This video was incredibly helpful! The visuals made it so easy to understand, even for someone like me who didn't finish high school and isn't a native English speaker. I rely on AI for translations, but this video is so well-made that it transcends language barriers. Thank you for making math accessible to learners around the world!

[@sumitasahu329]

OMG! This much of efforts just to explain vectors! your work is truly commendable. Thank you so much. :)

[@Erdem-hy9tt]

How someone dares to put an ad in the beginning of this outstanding video that says "Are the videos from 2006 really helping?"

[@hrithikmahato2401]

After an hour of struggle, I finally found it. ❤ You don't just teach the topic; you make it come alive.

[@jeromej.1992]

This is such a great initiative. I can't wait to watch it all. :) So excited!

[@asifhossain4265]

Physics "student", CS " Student" but MATHEMATICIAN

[@rickole7404]

physics and cs peasants, bow down to your mathematics overlord /s

[@tootaashraf1]

@@rickole7404 :( I'm a CS student. Although, I do have the same perspective as the mathematician student.

[@muhammadridho7680]

Is not fair Ikr

[@edumeli02]

@@tootaashraf1 yeah I'm a CS student too, honestly I have more of a mathematician perspective rather than the physics' point of view

[@maxwellsequation4887]

@@rickole7404 Joe

[@TanveerAlam-oe7yt]

Before watching whole lecture, I comment " Theses lectures might be the best to understand to linear algebra. Physicist perspective CS students perspective Mathematician perspective was awesome.... Thanks.

[@andeccan]

I watched this playlist two years ago in high school, after my teacher had finished covering this concept. Now, I'm rewatching it (along with the newly added videos) for my first semester, and I started crying because everything made so much sense! While crying, I remembered doing the same two years ago! Thank you so much for explaining things so well :)

[@yujinC_3PO]

Samee! I'm also rewatching this playlist in my 1st semester after watching it in high school.

[@andeccan]

@@yujinC_3PO It’s amazing how much more everything clicks now, isn’t it

[@yujinC_3PO]

@@andeccan It is 😌

[@zack_120]

6:11 - as always, really enjoy the amazing animations here. A small confusion in this particular video is the X and Y axes' sticks of 0.5 unit but not labeled. It'd make a whole word difference if sticking to the basic one stick-one unit labeling. Or, if necessary, at least label the sticks to avoid mistaking.

[@AltairCrysis]

Thanks, thought I was going nuts when moving "1 step to the right" suddenly changed visually from moving 1 tick to the right to moving 2 ticks to the right!

[@ahmedalsaati3408]

Only nine minutes but with big efforts (scientific material, auditing the material, script and graphics motion) with production management and then FREE for people. Thank you very much for teaching us.

[@shivangsingh5834]

I just wanna give you hug

[@Inspirtedmusic]

I can already tell that this video series is going to be phenomenal. Well done, ill see you on the next one!

[@SanjeetKumar-ky5yg]

Inspired Music

[@anupamkolay193]

WOW!!!!!!!! I have been struggling with these things, unable to visualize why things are happening and this video just clears all those up under just 10 mins!

[@sabrinapereira7673]

This is amazing. I feel like I've learned more with your 9 min video than my full 4 years of algebra in school. Thank you!

[@kietpham4635]

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

[@hodayfa000h]

So true lol

[@sanketkothari984]

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.

[@lamalamalex]

That awkward moment when you’re the physics student, mathematics student, AND the CS student 😅 and you had to deal with all three perspectives.

[@Sohlstyce]

rip

[@torkin4119]

So you are basically an engineer

[@jatinoham]

This is what happen when someone tries to code the physics for a game engine

[@cygnusdiwak4770]

i can feel that :(

[@purplegalaxy5265]

LOL Yessssss that would be me!!

[@saviocarvalho6126]

I am 53 years old and I am enjoying learning this stuff with my son. So well explained. Thank you,

[@jiachen8353]

thats so sweet

[@ShahZ]

these are timeless videos, whether you watch it 8 years later like I am or way into the future, basics of Algebra is immortal.

[@swapnilmahadik7112]

I am an atheist but right now I want a God to bless this guy. Keep up the good work!

[@mryup6100]

Lol that's funny

[@GyeonghunPyeon]

한국에서는 많은 학생들이 벡터를 고등학교 때 배우지 않는 쪽으로 교육과정이 개편되었습니다. 대학공부를 하면서 벡터는 필수적인 지식인데 이 영상은 그런 지식을 보충할 수 있는 좋은 기회를 마련해 주는 영상인 것 같습니다.

[@duck.5080]

강의 계획서에 벡터가 없습니까?

[@gyuro7988]

@@duck.5080 기하를 선택하지 않으면 벡터를 고등학교에서 배우지 않습니다. 고등학생들 중 7%밖에 기하를 선택하지 않고요.

[@thatkid-memeandedit2341]

​@@duck.5080 ഇല്ല അവർക്ക് Topics choose ചെയ്യാൻ പറ്റും

[@antidotejack2771]

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...

[@turquoiseninja4534]

I want to thank you for explaining this so well. I’m a visual learner and as a child I found math (especially word problems) fun and easy because I could properly visualize the process. I started to get really frustrated when I got older and mathematics moved on to more abstract topics since I had a harder time trying to “see” what the math was doing so your explanation was exactly what I needed.

[@physjim]

"numbers scale vectors, therefore scalars" OMG! My hole life is a lie.

[@uniqhnd23]

My life also wouldn't be enjoyable if it was a hole.

[@vol230]

@@uniqhnd23 lmaoo😂

[@ViratKohli-jj3wj]

@@uniqhnd23 best comment

[@vol230]

@Ray of HOPE have a look at the original comment he wrote hole in place of whole and then the reply

[@itona3165]

Ray of HOPE original comment says: (my HOLE life) It should be: (my WHOLE life) Hole and Whole are totally different words......google it XD

[@KaranTejwani-ft1bl]

The best teaching tutorial I have ever watched on linear algebra with Visual representation. Wonderful!

[@therealsuper5828]

i love how you explain stuff! as someone trying to learn game developing, vector math is the one thing that keeps giving me headaches. vector math is very common in game development, so making games is bound to always give headaches. i think i will learn some useful stuff from this series.

[@YonghaoHe-j9s]

hi how's it going have you learnt anything useful from this series

[@alxjones]

Great video, love the geometric approach to vectors. Can we get a music credit on these videos? Sounds like a Chopin Nocturne but I don't feel like listening to all of them to find it! Plus I'm sure I'm not the only one who really enjoys this music.

[@3blue1brown]

I suppose it is Chopinesque, isn't it? It's just a little bit that I made up. There's not really even a full song to it, just around 40 seconds to sandwich these videos with a theme.

[@alxjones]

Now that I listen again it actually sounds more like Debussy or Satie, either way I really like it! If you haven't, you should try your hand at composing full pieces of music.

[@xatnu]

Well maths and music are pretty similar skills. A mix of understanding the rules and knowing when to break them to get something new.

[@carrionpigeons]

That's a pretty generally-true description of every skill ever.

[@xatnu]

True. Bu somehow it seems like there's a strong connection between maths and music, who knows why :/

[@beaujamo]

When you started by differentiating the 3 views of vectors from different domains of study - super great intro!!!