Vectors | Chapter 1, Essence of linear algebra

Beginning the linear algebra series with the basics.
Help fund future projects: / 3blue1brown
An equally valuable form of support is to simply share some of the videos.
Home page: www.3blue1brown.com/
Correction: 6:52, the screen should show [x1, y1] + [x2, y2] = [x1+x2, y1+y2]
Full series: 3b1b.co/eola
Future series like this are funded by the community, through Patreon, where supporters get early access as the series is being produced.
3b1b.co/support
If you want to contribute translated subtitles or to help review those that have already been made by others and need approval, you can click the gear icon in the video and go to subtitles/cc, then "add subtitles/cc". I really appreciate those who do this, as it helps make the lessons accessible to more people.
Music: vincerubinetti.bandcamp.com/t...
Thanks to Elo Marie Viennot and Ambros Gleixner from HTW Berlin for contributing German translations and dubbing.
Thanks also to these viewers for their contributions to subtitles
Arabic: @Cewkins, Hazem
Bengali: Md Rasheduzzaman
Czech: @Chnapak
Greek: Nikolaos Tsagkas
Hebrew: Omer Tuchfeld
Italian: mattiacolucci
Spanish: Juan Carlos Largo
Thai: own doggoV●ᴥ●V
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If you are new to this channel and want to see more, a good place to start is this playlist: goo.gl/WmnCQZ
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[@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.

[@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😂

[@livingwithava5315]

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?

[@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

[@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!

[@ganeshgummadi7301]

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..

[@A_A_12_]

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

[@joesmith5970]

@@A_A_12_ no worries! This channel is great and I'm happy to support it.

[@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.

[@akibzuhairsamin2284]

@@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.

[@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.

[@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 😭

[@AlehzeySpidwagonovich]

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. 😢😢😢

[@shivangsingh5834]

I just wanna give you hug

[@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.

[@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.

[@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

[@olaoluwaolaniyi2241]

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

[@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.

[@cynthiabrantingham9999]

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.

[@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

[@krox477]

This is one of best explanations ever on vector math

[@japonjapon6242]

who you are?

[@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

[@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.

[@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.

[@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.

[@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

[@dailinelily]

Wait what Is this college stuff?

[@scienceium5233]

Me too

[@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

[@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!

[@GoldenRockefeller]

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

[@mesplin3]

agree

[@raumaankidwai]

It's the Grapher built-in application on Mac. It has built-in animation capacities, though it is hard to do.

[@deepakkumar99933]

liking this cuz 4:20

[@NoemeMatos77]

Nice observation!

[@elon.2193]

i thought all pakistanis thought of was bombing people @imran

[@user-ki3sb8st5p]

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.

[@akzork]

Did he just say he creates these animations through code?

[@danielwhiteside3610]

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

[@lanceang795]

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

[@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 :)

[@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!

[@professorx6328]

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

[@ManasMittal-pl6vg]

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

[@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!

[@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

[@tudatostrader]

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!

[@b1gb017]

Love that idea

[@aftereffects713]

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

[@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.

[@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?

[@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

[@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!

[@anusha8085]

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

[@Chadderbox]

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

[@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

[@danielelaprova4119]

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!!

[@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!

[@nunyabusiness3786]

You can no longer bamboozle me with your science for I have gained knowledge

[@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

[@phantomproduction5757]

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

[@TobySimone]

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!

[@japonjapon6242]

hello 😂

[@mavick.]

yeaah! I think the same!

[@thomasshaw6169]

This has to be my favorite math channel.

[@chuksjr.1440]

It definitely is!

[@rednax3788]

Holy shit do you actually make these animations in python wtf?! You could probs do it in After effects in a quarter of the time. PS: This video was really well made.

[@ThePheonix123]

his other vids are rly complicated and i think tht in those other vids its easier to just code it, plus with code much of the time u can reuse it

[@ProfessorEisenoxid]

+Gawsome Why do you know it is Python? :o

[@ThePheonix123]

+ProfessorEisenoxid oh its just alot of ppl ask and he gives the answer its python

[@ProfessorEisenoxid]

+Gawsome Ah, okay, he shows sourcecode. Sorry for being too inpatient. :D

[@ThePheonix123]

+ProfessorEisenoxid its fine :)

[@doejones48]

This channel is absolutely awesome! I'm a visual learner, and I sometimes have difficulty to understand some mathematical concepts...but now, I have the PERFECT visual representations to understand. Thank you SO MUCH!

[@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...

[@jadduajones]

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

[@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

[@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

[@kingshukcs]

It is absolutely amazing how beautifully u gave an introduction to this topic!

[@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

[@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

[@RohanPosthumus]

These videos are incredible! I ended up binge watching them all!👏🏻👏🏻👏🏻

[@Lucas_Simoni]

Years ago even before I found your channel, I thought how cool and helpful it would be to make math videos with mathematically precise animations. Your library is absolutely insane, I'm going to code math examples with it for me to understand better, and also because I'm in CS, to understand how to implement those formulas.

[@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

[@sumitasahu329]

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

[@gusiwanaga7380]

This video is just incredible. I wish professors in universities would teach like you! Just amazing!

[@puneetjain5625]

I have spent my last 6 years doing research in Linear Algebra and still it brings me joy to come here and see these visualizations!

[@ashutoshpadhi2782]

Aap kahan se phd ho bhaiya,

[@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!

[@jeromej.1992]

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

[@hannak1737]

oh my God how great you teach, thank you for this work so much

[@serious7179]

Thank you so much for this! I haven't taken an algebra class in about 22 years, and I'm trying desperately to change my career course to data analytics but I want to get a full understanding of linear algebra again first... I really appreciate the efforts and the comprehensive breakdown of your videos... You are a godsend!

[@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

[@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

[@MsThekiller02]

@@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

[@sabi7933]

This is the most beautiful educational video series ever. PERIOD.

[@umariktokyo]

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

[@scottmangiapane]

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.

[@liamsheridan8226]

My math teacher set this as homework for me

[@vpambs1pt]

That's awesome

[@siddharthrajan616]

you are lucky man. by the way my physics teacher recommended this channel to me!!!!!

[@joeyGalileoHotto]

Way better than memorizing the rote mechanics like most math teaches

[@constantines3238]

Our uni recommends this as a supplement part of linear algebra

[@teemiaoxin]

@@constantines3238 Same

[@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.

[@whitelotus187]

you are the best teacher on youtube.

[@odthegreatest]

I wish KZbin existed when I was in university. Such a lucky and unlucky generation right now. Like the Schrodinger's approach. Until you talk with them they are sharp and dumb at the same time. Yeah vectorsss

[@maazhassan5427]

Nice hair

[@antonhelsgaun]

This isn't uni level right?

[@alinac5512]

Gen zer here who really appreciates your perspective on us. The schrodingers approach is pretty accurate id say, even though I see a lot more negative/struggle overall.

[@howtodoit4204]

And a dumb generation I guess because we don’t see how big this is. Am woke but not others

[@theengineeringstudent2678]

Even so some students don't make use of this platform...

[@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!

[@irenzo5807]

Great video! Thanks for explanation☺️

[@RabiulIslam-tw6qc]

Literally, you are brilliant. The best way of teaching I have ever seen in my life.

[@RohanKumar-ex4rv]

Sir, you are a vector. Thanks for providing us magnitude and direction to do math easily. ❣️❣️❣️❣️❣️

[@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

[@christiansiebott6881]

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?

[@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.

[@goodcake05]

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 😇

[@istvantoth5466]

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 KZbin clip can help me to understand and move quickly to the next level.

[@marzipug5439]

​@@istvantoth5466 Keep it up :) Great to hear people your age are interested in ML.

[@prumchhangsreng979]

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.

[@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

[@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!

[@andrexeme_swag]

Blimey, the way you explain is simply masterful! I've watched plenty of your videos and still can't help but think to myself how terrific your videos are.

[@pekkariihonen8944]

I absolutely love this presentation style. This is quality. I've been looking for something like this for a while. Excellent work, and thank you!

[@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

[@ClaudiaCarranza1]

I struggled with Linear Algebra so much in undergrad.... by the end of the view, all the confusion from 12 years ago is gone. Thank you! I 'm even going to use some of what i learned to help teach vectors to my students!

[@user-bi6ez4mw4d]

09:10 [2x + y, x + 2y]

[@TazariaGaming]

Having been all three of those students, that analogy is absolutely perfect

[@ajchoppa4887]

Tazaria hello there brother

[@codinghub3759]

Same. I liked computer, I studied physics to create simulations, learned maths to understand the physics

[@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.

[@MindbendingRobot]

Amazing refresher! Thank you for establishing the context from the 3 points of view, Physics, Math, and Comp Sci. Vectors to me were the Physicist's view, from high school. So when my CS profs talked about them as a matrix or array.... I was stumped! Ugh... 6 years struggling! THANK YOU SO MUCH!

[@ahmadmahagna1255]

crazyyyy .... you programming these animations reflects a deeeeep understanding of math and Linear Algebra. Respect !

[@user-dw8lv6sy2y]

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

[@pradiptahafid]

GOD BLESS YOU!!!!! If I don't watch your video, I will fail my class!

[@augustolobo2280]

You can really make things I don't really understand, and find boring in college nice and fun. Amazing

[@parekshamanchanda8083]

Explained very well. I've been searching for a simple video on vectors for CS purpose, and came across the perfect one!

[@JesbaamSanchez]

Im taking Linear Algebra rn and I got to say Im learning wayyy better with your than what my professor can teach during class (emphasis on teach... He goes according to a book he doesnt even teach the class the book does)