Three-dimensional linear transformations | Chapter 5, Essence of linear algebra

Рет қаралды 1,966,612

8 жыл бұрын

What do 3d linear transformations look like?
Help fund future projects: / 3blue1brown
An equally valuable form of support is to simply share some of the videos.
Home page: www.3blue1brown.com/
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
Thanks to these viewers for their contributions to translations
Hebrew: Omer Tuchfeld
------------------
3blue1brown is a channel about animating math, in all senses of the word animate. And you know the drill with KZfaq, if you want to stay posted about new videos, subscribe, and click the bell to receive notifications (if you're into that).
If you are new to this channel and want to see more, a good place to start is this playlist: goo.gl/WmnCQZ
Various social media stuffs:
Website: www.3blue1brown.com
Twitter: / 3blue1brown
Patreon: / 3blue1brown
Facebook: / 3blue1brown
Reddit: / 3blue1brown

Пікірлер: 702

@shinequashie393 5 жыл бұрын

I count myself as one of the luckiest people to have stumbled on this playlist just before taking linear algebra in college

@realbignoob1886 3 жыл бұрын

That’s cool

@abeestosruinsageneration3725 2 жыл бұрын

Someone recommended this to me in the resources section in my class's study discord server. Already worth it on the first day of school.

@beytullahberk3632 2 жыл бұрын

same here

@zhilihuang6609 2 жыл бұрын

Yes, you are.

@suncho6502 2 жыл бұрын

I found it many years later :) Still, it's never too late to understand what I memorized back then.

@DekuStickGamer 8 жыл бұрын

I never thought I'd say this but I stay late up at night to watch math videos. These videos are incredibly intresting and rich with decription and fluid animation.

@jlpsinde 6 жыл бұрын

Me too, I sacifice some sleep just to watch these videos!

@huverdoose 6 жыл бұрын

*decryption

@attilabpc542 5 жыл бұрын

So do I

@stefanoctaviansterea1266 5 жыл бұрын

Same

@xiangli3322 5 жыл бұрын

Same, and now it is a quarter past 1 at midnight.

@AKSHAYKumar-gd7uq 11 ай бұрын

The composition of the two 3D matrices he shows near the end is 6-6-6 (top row) 33-44-55 (middle row) 6-10-14 (bottom row)

@mdayanali8885 11 ай бұрын

How

@AKSHAYKumar-gd7uq 11 ай бұрын

@@mdayanali8885 Check the last video about how to multiply 2 by 2 matrix and try same technique on 3 by 3 matrix For more clarity use online matrix multiplier to recheck

@mr.noodle6931 3 ай бұрын

Lesgo i got it right thanks

@leonaise7546 2 ай бұрын

@@mdayanali8885 Watch the last vid again

@AlexAsh25 16 күн бұрын

yesss after a failed attempt, i figured it out!

@enricoiraldo9057 2 жыл бұрын

I think the best way to use his amazing videos are: 1) watch his series on KZfaq to get a general idea of the mathematical significance of the topic 2) study on manuals/uni the details and the exercises 3) re-watch to wrap up and abstract from details for a last consolidation

@fahad_hassan_92 Жыл бұрын

Yup! Unfortunately, I had to deal with all the methods and rules for matrices, but preparing for newer topics like the way you have described is extremely helpful!

@anglaismoyen Жыл бұрын

I'm going to go through a LibreTexts textbook on linear algebra after this video series.

@LinhNguyen-nh8oq 10 ай бұрын

Yeh. that's actually what I am going to do !

@somebodyelse9130 Ай бұрын

I ended up doing it the other way around. I have been taking a university course in linear algebra, and watching his videos has been putting everything in perspective for me. I had just been memorizing facts and definitions of jargon without context, and using those facts to solve basically puzzles I didn't know anything about; now, I'm actually getting an intuition for how this relates to real vectors in space.

@KirillBezzubkine 4 жыл бұрын

There s one special spot in heaven saved for you. For helping all those math-lost souls and shedding light on their minds

@dingo4229 8 жыл бұрын

That feel when you've watched all the videos in this series the second they came out and can't wait for the next one to be released. Never been so stoked to hear how a person describes a determinant.

@MarkCidade 8 жыл бұрын

Me, too! Like wtf is that-you add up only the diagonal numbers or something and somehow that's the area of the parallelogram made by the column vectors?? This, I gotta see.

@GelidGanef 8 жыл бұрын

Yassss! I watched through all the Khan Academy videos on linear algebra. And I got it, more or less, they're great resources. But now actually I'm having fun doing this!

@noufalbarakati8854 4 жыл бұрын

AGREE

@jmiquelmb 7 жыл бұрын

I had a little eureka moment when I realised that the identity matrix is the only transformation that won't change the position of the basis vectors. This series of videos is amazing

@ababey1644 6 жыл бұрын

omg i had that too!!

@scriptkiddie7485 4 жыл бұрын

well yeah, to visualize a matrix is to take each column and say that it represents a basis so the identity matrix would just contain i hat, j hat, k hat, etc...

@padmasaran 4 жыл бұрын

Wow!! Never thought matrix was this intuitive!!

@nikhilnagaria2672 2 жыл бұрын

and also if a matrix has one or two columns like the identity matrix!

@esajpsasipes2822 2 жыл бұрын

@@padmasaran I'd say everything is intuitive, but the intuition might not always be intuitive. Why is everyting intuitive? Otherwise why bother?

@atriagotler 2 жыл бұрын

This series is a true masterpiece. I mean whole 3b1b is awesome, but this playlist just sits in a league of it's own. This should be the gold standard for all linear algebra classes. Also, linear algerba should be introduced much much earlier. It's not that complicated if explained in a common sense manner as you can see!

@danielrabinovitz478 3 жыл бұрын

I just want to genuinely thank you for saving me in my Linear Algebra class. Your style of teaching is extremely simplistic and fluid. I'm remembering why love math so much even when classes frustrate me immensely.

@dynamicgecko1213 2 жыл бұрын

I just now realized that the reason the identity matrix is a neutral element in matrix multiplication is because it is the default values for each basis vector (i, j, k, etc). It transforms every vector back to itself. It makes so much more sense now! Man, this series is amazing. Thanks!

@markostojanovic5930 Жыл бұрын

Our linear algebra prof. always shares a link for one of your videos in this series at the end of every chapter in his skript because he is a big fan of your videos. I think that‘s great and we have a much better intuition for this topic, thank you!

@ExCoSeH 8 жыл бұрын

Omg you deserve my money more than my teachers!! What is your PayPal??

@sillymesilly 7 жыл бұрын

I also want to donate to him.

@lucciopreso1 6 жыл бұрын

it's a little boring to create an account. Do you have btc/bch/other crypto address?

@carterfogelman4613 5 жыл бұрын

@@lucciopreso1 "I want to donate in a way that's easy for me, not easy for you."

@puckry9686 4 жыл бұрын

@@carterfogelman4613 what do mean easy

@Paul-qn7qv 4 жыл бұрын

@@lucciopreso1 He is a verified Brave creator. You can tip BAT to him if you use Brave browser. I just tipped him :)

@seanm9306 8 жыл бұрын

And now I understand identity matrices

@IX0Ahmed0XI 7 жыл бұрын

Oh god! Everything started to click once I read this comment! Like I understood what the video was saying but it never came to my mind how identity matrices make perfect sense now because of this video :D

@daredo2 7 жыл бұрын

i agree wow

@cameronfitzpatrick2489 6 жыл бұрын

Yup - so why does finding the inverse using the identity matrix work the way it does? Using rref of [A|I] to making [I|A^-1] - using the identity matrix should make much more sense now too

@carbon273 6 жыл бұрын

Wait explain? I think it flew over my head

@lazypunk794 6 жыл бұрын

In and identity matrix, the main diagonal elements are 1 and others are zero. Which means after transformation, the basis vectors remain in the same place.[the first column is 1 0 0 , second is 0 1 0...]. This is why a vector remains unchanged when multiplied by identity matrix.

@marciomaiajr 6 жыл бұрын

There's an old programming book titled "flights of fantasy". The author uses a lot of matrices for the 3d calculations and finally now, 20 years later, I understand why.

@tobibello4160 6 жыл бұрын

At this point in the tutorial, I just want to give you all my money. You've made my mathematics make so much sense, I feel like a child with an endless supply of candy!

@whimsicalkins5585 Жыл бұрын

Me too!😆😁

@frankdimeglio8216 Жыл бұрын

@@whimsicalkins5585 WHAT IS E=MC2 is taken directly from F=ma, AS TIME is NECESSARILY possible/potential AND actual ON/IN BALANCE; AS ELECTROMAGNETISM/energy is CLEARLY AND NECESSARILY proven to be gravity (ON/IN BALANCE); AS the rotation of WHAT IS THE MOON matches the revolution. Consider TIME AND time dilation ON BALANCE. The stars AND PLANETS are POINTS in the night sky ON BALANCE. The diameter of WHAT IS THE MOON is about one quarter of that of what is THE EARTH. On balance, the density of what is the Sun is believed to be about one quarter of that of what is THE EARTH. Excellent. Consider what is THE EYE ON BALANCE. The TRANSLUCENT AND BLUE sky is CLEARLY (and fully) consistent WITH what is E=MC2. WHAT IS THE EARTH/ground is fully consistent WITH what is E=MC2. CLEAR water comes from what is THE EYE ON BALANCE. Notice what is the fully illuminated (AND setting/WHITE) MOON AND what is the orange (AND setting) Sun. They are the SAME SIZE as what is THE EYE ON BALANCE. Lava IS orange, AND it is even blood red. Yellow is the hottest color of lava. The hottest flame color is blue. What is E=MC2 is dimensionally consistent. WHAT IS E=MC2 is consistent with TIME AND what is gravity. What is gravity is, ON BALANCE, an INTERACTION that cannot be shielded or blocked. Consider what are the tides. The human body has about the same density as water. Lava is about three times as dense as water. The bulk density of WHAT IS THE MOON IS comparable to that of (volcanic) basaltic lavas on what is THE EARTH/ground. Pure water is half as dense as packed sand/wet packed sand. Now, the gravitational force of WHAT IS THE SUN upon WHAT IS THE MOON is about twice that of THE EARTH. Accordingly, ON BALANCE, the crust of the far side of what is the Moon is about twice as thick as the crust of the near side of what is the Moon. The maria (lunar “seas”) occupy one third of the visible near side of what is the Moon. The surface gravity of the Moon is about one sixth of that of what is THE EARTH/ground. The lunar surface is chiefly composed of pumice. The land surface area of what is the Earth is 29 percent. This is exactly between (ON BALANCE) one third AND one quarter. Finally, notice that the density of what is the Sun is believed to be about one quarter of that of what is THE EARTH. One half times one third is one sixth. One fourth times two thirds is one sixth. By Frank Martin DiMeglio

@Cleisthenes2 2 жыл бұрын

All I can say is that if I were a mathematician, I would have three hats and call them i-hat, j-hat, and k-hat.

@mrlaul7130 2 жыл бұрын

4:15, yes but I don't have a graphic card in my head

@bungeruwu 8 жыл бұрын

Is that right? 6, 6, 6 33, 44, 55 6, 10, 14

@denascite2029 8 жыл бұрын

yes

@SebastianLopez-nh1rr 8 жыл бұрын

Got the same

@reinux 7 жыл бұрын

i hate arithmetic.

@leonardofilippini 7 жыл бұрын

same, i love these videos my god

@musamwinyi2049 6 жыл бұрын

wrong

@scriptkiddie7485 4 жыл бұрын

Wow, I'm speechless. In a matter of hours, these videos caused me to go from hating linear algebra to one of my favorite subjects. At my high school, since not many people are advanced enough to do linear algebra, we have to teach ourselves. There are about 20 or so kids in my class and we each alternate teaching the class, and everyone is new to teaching. So, we ended up doing about 6 numerical theorems for every section without thinking about it, many without proofs. I was desperate for some type of visualization of linear algebra, and I just found the complete gold mine.

@romanalaivi6967 2 жыл бұрын

I forgot essentially all math from my school days. The way you explain this makes me realize there are actually many weak analogies to daily life and other tasks I've done like balancing a gimbal on each axis first. Amazing how intuitive this all is for someone whose forgotten just about everything and trying to get into machine learning. Thank you so much for making this so incredibly easy to understand. I feel lucky to have found these videos.

@teddybrow 3 жыл бұрын

Five years after the initial release, I'm watching this series a third time around. It's a great refresher and a compelling watch every time. Thanks, Grant!

@djec-eazy1229 2 жыл бұрын

Your ability to create fluid and intuitive animations to represent a topic is incredible and never ceases to add richness and clarity to a topic. Thank you for everything

@noufalbarakati8854 4 жыл бұрын

I've been studying, working with and even teaching linear algebra for years. This series blown up my mind. Thank you so very much.

@TimCutts Жыл бұрын

This is so clear. I remember learning this in A-level Maths when I was about 17, and using it to write a computer program which would display a wireframe globe of the Earth in any orientation. But we were taught the formulae by rote, the words "basis vector" were never used that I can remember. I'm learning this again now, more than 30 years later, so that I can get to grips with the basics of quantum computing, which seems to depend very heavily on linear algebra.

@kabeerkumar4334 3 жыл бұрын

The intro and outro music creates an emotional bond with this channel and grant... It's like a lullaby :')

@wackywally69420 3 жыл бұрын

my linear algebra course has been taught in the reverse order - matrix properties first, then transformations. its like a bunch of random theoretical stuff that doesnt seem to be related thrown at us but watching your videos puts it all together so simply.

@dhidhi1000 7 жыл бұрын

I can't believe I'm actually gonna have any sense of what the heck determinant is

@taprusthe3rd496 8 жыл бұрын

For the matrix multiplication at the end i got 6 ; 6 ; 6 33;44;55 6;10;14 Seems about right

@yaeloosthuizen725 3 жыл бұрын

can confirm

@Test-ri2kr 3 жыл бұрын

@Yael Oosthuizen Can you explain the steps please?

@yaeloosthuizen725 3 жыл бұрын

@@Test-ri2kr you have a b c |0 -2 2| |0|. | 6 | |5 1 5| |3| = 0xa +3xb + 6xc=|33| |1 4 -1| |6|. | 6 | That's for row one You also do: For row 2 1xa + 4b + 7c For row 3 2xa + 5xb + 8xc

@esajpsasipes2822 2 жыл бұрын

i had an error in there but i was able to find and correct it. I got the same result.

@guywhoistooparanoidtousere3758 2 жыл бұрын

Would it be correct to say that i-hat after the first transformation is [0,3,6] and after the second transformation it is [0,5,1]? Am I understanding that right?

@Math_oma 8 жыл бұрын

The power of abstraction.

@adultishgambino8713 3 жыл бұрын

yes

@lexalious47 4 жыл бұрын

I wish I'd stumbled upon these videos earlier than 3 hours before my math final.

@shaon56 3 жыл бұрын

If you study solid mechanics or finite element anlaysis, then this transformation using matrices gets pretty clear. You break down a structure into points and apply the stress and shear equations between the points and convert them to matrices to get the answer. But even though I did not realize that this is what it actually means when we do matrice multiplication in mathematics. Thanks for the videos. You have explained very nicely!

@TheHippyhopp 8 жыл бұрын

just finished a semester with some linear algebra, but now i want to go back and try more

@sealol5209 6 жыл бұрын

Thank you so much for this video series, feels like i've been cheated by my teachers for only learning how to memorise formulas and not have any understanding further than that.

@romance177 5 жыл бұрын

i enjoyed every second in this series. you explained the material better than any professor I have encountered during my bachelor and master degrees. well done.

@harishjain2612 6 жыл бұрын

After tirelessly working on my project in robotics, I never really gained a good understanding of the 3d transformations, which is ubiquitous in robotics.Your videos have greatly helped me in visualising the math behind the transformations. Thank You.

@fancyphysics8458 Жыл бұрын

Two years ago, I had to learn Linear Algebra as a core subject in my university. I hated it because neither did I know whats going on nor my professor put any effort to teach us properly and thats happened all it was online classes because of Covid- 19. I surely had to memorize tons of formula without understanding to pass this exam. Now I am glad I am finally understanding this concepts little by little. Thank you so much for this 😊😁

@RandomTot 4 жыл бұрын

Thank you soo much 3blueonebrown, i have for five months tried to come up with a formula that does exactly this. I got pretty close even though i did not not anything about linear algebra just some trigonomerty i have been studing by my own. Thank you so so much this really helped me with my boid experiment i am cunducting in unity.

@ljzilchz6548 2 жыл бұрын

I once asked my teacher "what is the real purpose of learning matrices and it's applications in real life and how should I visualise it? " But All he ever said was "it is not really applicable in real life and he added that I should just practice hard to be good at it". After all these years, I finally got all my questions answered. Thank you soo much bro.

@Jame5Mead 8 жыл бұрын

Thank you for making these videos. They helped me to properly visualise what's really going on.

@vivekjain8181 Жыл бұрын

I never really understood what matrices represented or what linear transformation actually meant. It was my lucky day when I randomly just started watching these videos. These are absolute gold! Anybody who thinks mathematics is all about arbitrary number crunching will have a change of heart. The meaning of an identity matrix (diagonal matrix with 1s) is so clear after watching this. Basically the basis vectors remain at the same place before and after transformation and hence the multiplication with another vector/matrix results in that same vector/matrix!

@estefaniakiara-elizabeth8538 7 жыл бұрын

Thank you so much for this footnote, it totally helped visualize 3d space, totally love your series.!!!!

@shiyi9993 7 ай бұрын

This content is literally GOLD! I always don't understand the point of exam just for the sake of exam, but I absolutely love digging into reasons of "why"! Haven't enjoyed this kind of joy of pure learning for soooo long since college!

@iloveblender8999 Жыл бұрын

Thank you very much! These videos are so much better at showing what the maths does than the text in those math books. Yeah, I still have to read them to get used to the more formal stuff, but having a visual idea is gold.

@mnada72 5 жыл бұрын

I wish I have knew these and other concepts earlier in time , may be I would see the world differently. Thanks for the most appreciated effort spent in theses videos. Hoping to see more

@Supware 8 жыл бұрын

I think there's a typo at 0:46 (peek*) unless there's a pun I'm missing. Loving this series man (: your best videos yet

@3blue1brown 8 жыл бұрын

Uh...yeah...totally meant that 3d pun :)

@vicente8749 8 жыл бұрын

Yay! Without using any formula! :)

@odyseuszkoskiniotis6266 4 жыл бұрын

@Trevor Carey It's very helpful to visualize 4D I recommend it

@babbetteduboise4284 4 жыл бұрын

I was going to type the same thing--3 years later :-) !

@emilnavod67 3 жыл бұрын

@Trevor CareyIsnt it a book

@stormer7502 3 жыл бұрын

These are amazing! They clarify so much of what ive observed and figured out. I hated math in school because the derivations were never taught, but out of my own interest ive invested myself into things that require it and now i even find math itself fun and fascinating. So many years shamed for not getting any of it. Im sorry that i couldnt get my younger, blissful self to remember or even try to remember what might as well be arbitrary bs.

@abdallahhashem5135 4 жыл бұрын

Those videos are really inspiring. I've never thought of Linear algebra like that before. I'm just imagining how that was essence. for programming like for example when you search something using your name or ID number it does some sort of matrix manipulation(based on your program) and points to SSD where your information is.

@ChethanSrinivas 4 жыл бұрын

Excellent, this should be the way that is to be taught at engg schools, tensors is one of the most important topics for engineers. loved the whole linear algebra series ( I liked all of 'em). Typically used for 3d stress transformations and even mass inertia matrices, however this can be used for 2d stress transformation as well, but usually also done by trigonometry. Man you are a boon to lot of people like us, thanks a ton x (1/0). Have a great day.

@user-kz5kt9wj1c 15 күн бұрын

This is the best linear algebra lecture I've ever watched

@kjekelle96 4 жыл бұрын

0:00 intro 0:13 background 0:52 3D linear transformations 1:56 3x3 matrices, and example 2:49 correspondence 3:29 composition, and applications 4:03 homework

@spelunkerd 4 жыл бұрын

I love the way this dissects each of the original basis vectors into three elements. Then the product of those with the new transformation determine where the new basis vectors will lie. Even so, for juggling all the relevant details, it is still helpful as an accounting aid to remember conventional multiplication patterns. I guess that says something about human memory.

@siddhantdeshmukh7120 3 жыл бұрын

ok so when you turn in a video game you are essentially rotating the whole environment around you in the opposite direction. To do that you are multiplying every vector of every object in your environment by a matrix which is the transformed version of the original view's basis (now I understand why do some graphic developers use the term rotation matrix ).And if you turn again, you transform the transformed vectors and keep on doing it every time you turn. Oh my god this is really EXHILERATING. Much appreciations for the content, very good content.

@alistairbaker4282 6 жыл бұрын

Thank you so much for your videos. They are incredibly well done. I've shared the Essence of LA with other software developers in my company. If you are able to produce a video about how homogeneous coordinates can be used to represent both position and orientation of an object and transformations of that object, that'd be totally awesome.

@gnuPirate 3 жыл бұрын

Just going through the play list, leaving repetitive thank yous for this AMAZING CHANNEL! I really appreciate these. Thank you.

@viratzz 5 ай бұрын

Oddly enough this video on 3d transformations was what finally enabled me to have Linear Transformation as a concept click into the place! Thanks for your work.

@MH-oc4de 5 жыл бұрын

I learned linear algebra a long time ago and I still use matrices and transformations, but these videos have helped me visualize them in ways I never did. Thanks!

@movahediacademy9017 8 жыл бұрын

Fantastic videos. I'm a detailed oriented person that needs to know why things work the way they do, and not just brute force through calculations blindly. This helped a lot. Looking forward to newer videos.

@JerikRiza 8 ай бұрын

linear algebra has taken its toll on me this semester, I'm going through this entire playlist during my readers week right now.

@scottdotjazzman 5 жыл бұрын

This just made sense of the hours of struggling I experienced with the XNA game studio way back in 2010. _MAN_ I wish I'd had this so clearly demonstrated back then!

@Felipe-sw8wp 8 жыл бұрын

Very simple and clear, with pretty coordinate system images. Nicely done.

@darthdenco 8 жыл бұрын

This has helped me more with Lin. alg. yet than the semester with my professor. Great videos, thank you for uploading.

@aminpakshir5528 6 жыл бұрын

it all started with a click on a video on the youtube and now I have got to the 6th one!!! amazing!!! great job!!! probably I will not leave until I cover ALL OF YOUR VIDEOSS !!! THANK YOU!!! I make robots and this was exactly what I wanted...

@PG-uv6lq 7 жыл бұрын

Hey! These videos are too good! Keep up the great work:)

@Daddy_Skeletor 2 жыл бұрын

I am baffled at the fact how understandable these videos make linear algebra, if only I had discovered them sooner. Thank You!

@snehalthanekar8728 3 жыл бұрын

I am feeling very happy and empowered.Hats off to your efforts!!Thank you so much!

@Titurel 8 жыл бұрын

this is one of your best series!

@adolfocarrillo248 5 жыл бұрын

Simply beautyful work done here. Thanks to 3Blue1Brown

@rishisharma5827 2 жыл бұрын

I watched these when they first came, and now revisiting for uni mathematics. Your explanations are much more intuitive than my textbook.

@jujumx1716 4 жыл бұрын

I do really really thank you. You are the best teacher I've met so far. Your videos are dramatically helpful that I understand Linear algebra.

@tbaiyewu 7 жыл бұрын

This is the best video ever on youtube and trust me I use youtube a lot. you have put a lot of work into this. thanks for sharing.

@itfrom 5 жыл бұрын

you saved me! Thank you for your great visual works.

@manijakhatun4565 7 жыл бұрын

thanks for these concepts.. i really love them..

@shanawazkumbari4122 4 жыл бұрын

thank you for making it so intresting and beautifully explained

@felipegetulio 6 жыл бұрын

Really good video! I would love to see a video about Quaternions as well! I think they're amazing mathematic tools for 3D rotation, and honestly, I don't really understand how they really work 😥. It would great if you explain it in one of your videos, I really enjoy them😄

@mohammedkhalid9317 5 жыл бұрын

I was stuck trying to understand Linear Algebra without going into too many details until thankfully I found these videos, THANKS ALOT

@TJGalloway1 8 жыл бұрын

I really appreciate you making these videos.

@motazart5961 6 жыл бұрын

Your opening quote led me down a rabbit hole! But I'm back after 7 hours..and I have a new favorite TV show.

@maxscribner1743 7 жыл бұрын

You should talk about Quaternions in a side video

@Carutsu 7 жыл бұрын

please! I've used them before and I have no idea why they encode a 3d rotation

@OttoFazzl 7 жыл бұрын

Yes, please do quaternions.

@humanbot4 Жыл бұрын

I always had a problem in multiply 3 by 3 matrix in my high school. And now I stumbled into your videos about matrix, and I finally understood what it actually means. Thanks you very much.

@anahitaabdollahi4584 10 ай бұрын

Watching this for the 4th time! I cannot begin to explain how much has this series helped me❤

@davidm.johnston8994 7 жыл бұрын

I was gonna say that the rotation wasn't about y but then I realized y is represented by the red vector and x by the green vector. It's very misleading for someone who spends his life working in 3D software like I do haha.

@davidm.johnston8994 7 жыл бұрын

Usually it's : x: red y: green z: blue

@totallycarbon2106 4 жыл бұрын

Mentioning handedness here could have been good too

@tombailey4262 6 жыл бұрын

These videos are brilliant...hats off to you!

@ANabih-uo3zy 2 жыл бұрын

I couldn't grasp linear algebra fully in my robotics courses, so here I'm . very glad to find this playlist

@stawag3478 5 жыл бұрын

Simply put, you enlightened me, thank you

@rajaparameswaran1119 Жыл бұрын

How do you make the vectors and the coordinate system dance so well to your music? It is such an impressive way to learn Liner Algebra.

@user-dw8lv6sy2y 3 жыл бұрын

3차원에서의 비선형적인 함수나 그래프등을 선형적으로 표현시키는 것에 대해서 알 수 있었습니다. 미분방정식을 풀 때 비선형적인 항이 많이 나와 힘들었었는데 덕분에 방정식을 풀 수 있었습니다.

@ericfu8 5 жыл бұрын

this is just so incredible explanations !

@anonymoususer4356 4 ай бұрын

Thank you very much. Had zero intuition about the subject until these videos.

@OmarAhmed-od9rf 5 жыл бұрын

That was really helpful! Thank you

@shashwatbhatnagar659 2 жыл бұрын

Sir your teaching is literally giving me goosebumps everytime, thanks a lot sir.

@faiz_uddin Жыл бұрын

Felt lucky to come across this beautiful playlist.. Thank you very much...

@AltairCrysis Жыл бұрын

Note: For anyone else who's confused, at 1:38, each tick on the graph represents 0.5, not 1! That's why each of the "unit" vectors (i, j, k) are shown with a length of 2 ticks.