The Applications of Matrices | What I wish my teachers told me way earlier

[@chaselongenecker5398]

Modern mathematics education’s biggest crime is not explaining what the hell anything is useful for before you learn it.

[@MathTravels]

Absolutely. It goes with earlier concepts, too.For example, the context is rarely given for fraction operations (like division) and when it is it's inadequate.

[@MrAlubenco]

Too right... math is extremely fun when it's applications are made known...

[@AyushSingh-be2nm]

Get a dive into the Jee mathematics and Its Teachers. You will Feel It. In India many things are like festival. Onen of them is Jee exams.

[@abyasahasan]

yessss

[@jianhuang0124]

Math itself has nothing to do with applications. It's a pure logic game. Applied cases will distract the core.

[@martinmartinmartin2996]

As an electronics engineer that dabbles in math: For 30 years I have puzzled: WHAT IS an eigenvector ? Finally (for the first time, after 40 years ) I have UNDERSTOOD ! Thank you !

[@lonestarr1490]

Fun fact: "eigen" in German means something that is inherent or a personal attribute by something or someone - not as a verb, but as a prefix. For example, you can translate "peculiarity", "individuality", or "foible" to "Eigenart" or "Eigenheit" in German. And an "Eigenschaft" is something like a characteristic property or an attribute.

[@ccuuttww]

OH what 40 years I think u miss the lesson of PDE and ODE it will explain what is eigen space

[@rigorouselectronics8089]

Look at 3Blue1Brown's linear algebra playlist. You'll get a more full understanding of the concept. While you're there you might as well check out the most beautiful equation, which you and I use alot as electronics engineers (particularly in electromagnetics and signal processing)

[@GodzillaGoesGaga]

Totally agree. We never got an explanation what they were either.

[@StephenGillie]

This video really fills in some of the gaps in connecting Pythagoras to Minkowski, through Einstein, to Kaluza-Klein, String Theory, and beyond. Just keep adding dimensions onto the matrices for different fundamental fields.

[@khari_baat]

Dear Zach, I thank you from my heart. This video alone is worth more than years spent in mathematics. I remember multiplying matrices by matrices and answering questions in exams without ever understanding what are they trying to do. The education system sucks big time.

[@randomrandom316]

As a fellow Indian, we the students suck just as much. When a student is really interested in the class and asks the teachers why we are learning a particular topic, what its applications are and so on, most students simply roll their eyes and look at that student as if he/she is a criminal. Most students don't mind copying assignments and are literally willing to cheat on the exam to get a higher score, never stopping to think if they are pursuing education for learning or for the sake of some place in social hierarchy. Education system indeed sucks big time, but frankly, a lot if it is really a reflection of the students themselves, if students held themselves to some principles and standards maybe they can legitimately seek redressal from the system, else the system knows where our priorities really are and they are more than willing to exploit it.

[@impolitedirector3595]

@@randomrandom316 Can't agree more

[@josefrancis7126]

ESPECIALLY IN INDIA

[@DoctrinaMathVideos]

You have to understand how to work with matrix computations and understand vector spaces before you learn the applications and this is the goal of a beginning linear algebra course. After developing a solid foundation in linear algebra then you can take a more advanced linear algebra course and this is where you will learn all about the applications of linear algebra (even more than what's covered here in the video).

[@ungarlinski7965]

Or you're an idiot for not recognizing it's use. Or you missed that part due to being on your phone in class. Or you never read your book. Or you should have just gone to trade school.

[@cfgauss71]

Showing how matrices can be used to blur images was awesome. As a civil engineer, I should add that matrices are also used to analyze entire structures (building, bridges, etc), where a force matrix (ex: the loads the individual beams or columns experience) is equal to the product of a stiffness matrix (reflects the material properties) and displacement matrix (how much the members of the structure move). In effect, it's Hooke's Law, only taken to an extreme level using matrices.

[@JohnFekoloid]

You're talking about FEA. But really, it's all coded into the computer software. Most likely, it will be easy for the average user not to even know about any matrices in there and just use the software.

[@GoldenAgeMath]

Would these "matrices" really be tensors? Asking as someone who studied physics but not engineering.

[@rkus07]

@@GoldenAgeMath Theory of Elasticity uses a lot of tensor math.

[@alibaba-kv1ww]

@@GoldenAgeMath Hm I would say not every matrix would be really considered as a tensor of a 2nd order.I mean, mathematically they are but let's just take an example of a 3dimensional state of loading.The Hook's law would be represented with a 4th order tensor(material properties)acting on a 2nd order tensor(strains) and that would give 2nd order tensor (stress). But take the node matrix for example. Is there any physical meaning behind or not? It's just a convenient way to write all nodes in a Matrix form and therefore we won't really say - it's a "node tensor" right?

[@twinplayerz]

I am taking Analysis of Structures right now and this is the last topic that is being covered in this class. In a conversation with other peers who have taken this class in the past, they didn't even cover this topic!! Thanks for sharing your insight!!

[@patrickmayer9218]

Notes: *Vectors that are only scaled by matrices are called eigenvectors of that corresponding matrix. *How much the vector is scaled by is called the eigenvalue. *Blurring, distorting, and sharpening images all use very specific matrix math on the pixels to get the desired result. Thanks for the video, Mr. Star!

[@sebastiangudino9377]

You might learn more on the last mentioned cases by learning about convolutions. 3b1b has a video about that (And also a great series for all of linear algebra). Also in PDE's you will find an operator called the laplacian. And for numerical simulations on a discretized grid we use a matrix very similar to those for computation. I think in 2D this method is called a 9 point lattice

[@patrickmayer9218]

@@sebastiangudino9377 Thanks for the info!

[@Zilberlex]

He did not explicitly say it, but seeing the number of graph triangles in the last part basically allows you to calculate for potential threesomes.

[@anothrto1045]

It also explained how p{2,3,4,5,6} got STIs from p1

[@matthewcuriel991]

Lolol

[@cancel1913]

@@anothrto1045 I thought it was STD's but what do I know

[@anothrto1045]

@@cancel1913 infections also covers things that aren't diseases and in addition some syndromes aren't diseases but result from infections

[@bobloblaw1021]

Bow chicka wa wa

[@jonny2575]

*No one:* this video is getting long and uninteresting.. *You:* “As much as I’d love to keep going into depth on different subjects, this video is already quite long.” You sir are a gentleman and a scholar. PLEASE make a part 2.

[@dennispetrov9628]

I for one just recalled how I lost track halfway into the lecture, just like I did this time with this video. Now it would take me hours to digest that second part, that is, if I were in the mood. Is there a math course for bipolars with ADD? I mean, serving it in small chunks is a real help for some.

[@timinator1178]

@@dennispetrov9628 do one video a day from Khan Academy is what I'd suggest. One video a day, solving one problem a day, and eventually you'll grease that math groove enough that you can move to two problems a day, then three, then two videos a day, etc. I don't know, just a suggestion. I know Khan breaks everything into tiny bite sized videos overviewing single concepts.

[@dennispetrov9628]

@@timinator1178 thanks, maybe I will. It's not that I'm plain stupid, it's just that I'm a bit bipolar and a bit ADD , that's what's slowing me down

[@timinator1178]

@@dennispetrov9628 I understand completely. Everyone learns different ways. Some are more advantageous than others, but there's always different a method that works better for someone. Personally I think it's very interesting, all the different ways people learn. One of the problems of this internet age is that so many people go through school thinking they can't learn or they aren't meant to be knowledgeable, when the real problem is that they simply don't fit in a one size fits all approach to learning. Many people need an optimized approach, and finding that approach isn't always easy.

[@tyereksmith8946]

The internet is so wonderful just imagine being a million miles away and find a great teacher like you who isn't boring. Great job nuff respect from kingston jamaica 👍🏾

[@cubingcubez6678]

i m from India

[@cboy-ou2hr]

The internet truly is amazing I envision a day where traditional school settings will finally be obsolete and u truly get a education worth while

[@BangMaster96]

+tyrek smith You can't possibly be a million miles away from anyone on Earth, the Earth's diameter is less than 8k miles.

[@bobloblaw1021]

Imagine all the people, living for todaaoouuy. You may say I'm a dreamer, but I'm not the only one. I hope some day you'll join us, and the world will live as one. PS silly Google doesn't know that song. Hey look ma I made it!

[@connellitblog]

Trinidad

[@turpialito]

Zach, people like you should really have a voice in public education policies. My sincere congrats.

[@Bald_Zeus]

I'm studying to become a mechanical engineer and I've really struggled with linear algebra, mostly because I haven't grasped how I need to view it. This video helped me immensely

[@dixonhill1108]

Yeah I can use it, but I never had a successful way of seeing it in my head. Pretty rare in mechanical engineering to not be able to imagine the thing, that's a problem for electrical nerds.

[@panself]

3blue1brown makes much better visual explanations.

[@BigDaddy-je2nq]

When I took linear algebra nothing had a purpose, it was just memorizing a pattern, I didn’t even realize what a matrix was until I went off on my own experiments with information I didn’t even have to pay for

[@The_InfantMalePollockFrancis]

I'm studying mathematics and physics for an entrance exam to a university for an engineering degree, but really I need the scores for pilot school and I WANT to visualize them--at least to a degree that a good pilot could use--and I'm finding it quite difficult

[@The_InfantMalePollockFrancis]

I'm studying mathematics and physics for an entrance exam to a university for an engineering degree, but really I need the scores for pilot school and I WANT to visualize them--at least to a degree that a good pilot could use--and I'm finding it quite difficult

[@felipeflores5403]

Man, you talked about pandemics and riots and I'm here watching this in June 2020 convinced you're an actual prophet

[@brian8653]

I know, he's a prophet or something

[@gerooq]

@@brian8653 This reminds me of the time mathematicians in the old ages were called witches

[@aschmitt89]

THIS!!!

[@aschmitt89]

If mathematicians in old ages were called witches, and today we're calling them prophets... Is our universe really real? Or could it really be that we're all part of a massive calculated simulation?!?! (I've literally only heard this conspiracy theory once before in my life, but DANG Math can be scary accurate at times!!!!)

[@stevencvisuals]

I see how matrices can be used now lol we're stuck in a pandemic

[@sdeerwester]

I'm one of the authors of latent semantic indexing/analysis, which is a technique that some folks in natural language processing, machine learning and search engines have found useful. It's based on some pretty funky linear algebra. I just wanted to say that, even with the major role that matrices in general and linear algebra in particular have played in a very important chapter in my life, I still learned things from your intro. Very nicely done.

[@polyhistorphilomath]

LSA? You’re the man

[@aBradApple]

I curiously took an online course for linear algebra thinking it should be a walk in the park and LSA blew my mind. Though unintentional, I found it improved my programming and understanding of matrices. Thanks a lot for your contribution to society.

[@darknightninja9773]

Matrices are a crucial part of 3d graphics. In my graphics game engine that i am writing from scratch, all the mathematics related to transforming, rotating, scaling and even projecting the scene onto the screen is handled using matrices. I too was really surprised that matrices can be so useful when i was first exposed to graphics programming. Its sad that they dont tell you stuff like this in school.

[@skilz8098]

Most of those who don't work with 3D Graphics don't understand the significance of the MVP... And not it's not Most Valuable Player either. It is the combination or multiplication of the Model, View and Projection Matrices. And depending on how you defined your 3D coordinate system L-hand or R-hand system will determine the order of linear transformations that need to be applied such as translation, scaling and shearing and rotation about an axis. This also doesn't account for the fact of transforming one set of data in one coordinate system to another. For example; transposing the coordinate values of a Model's vertices, normals etc. from model space into world space and from world space to camera space and from camera space to culling and clip space and finally from Camera or Eye space to Screen Space in which you can not forget the perspective divide otherwise 3D Images mapped to a 2D Screen will looked stretched and skewed. This still doesn't account for triangulation and the vertices winding order for back face culling, this also doesn't account the Z-Depth buffer and the order of rendering of objects that are dependent on two major factors, first the depth and second if it has transparencies or not... Then after all of that comes all of the lighting calculations as there are 3 major types of lights; point or positional light, directional light and spot light as they all share some similar commonalities but each have their own distinct properties. For example a point light could be that of a street lamp as it has a position and the light goes out in all directions. A directional light such as the sun or moon in a sense doesn't have a relative position but comes in from the same direction. The spot light is like a flash light as it has both position and direction but it also has attenuation and cutoff angles. Lights also can contain colors which can be defined as a vector of values. This also doesn't account for all of the different kinds of lighting and shading techniques that one can achieve such as bump map, glow, blur, reflection and refraction, bloom, and so much more. So if you are trying to use modern OpenGL with GLSL, DirectX with HLSL or Vulkan with Spir V and you are trying to build a 3D or even a 2D application while using Shaders to be sent to a modern GPU and you don't understand linear algebra, geometry, vector and matrix calculations along with trigonometry and vector calculus you are going to be at a loss and you might start to pull out your hair trying to get everything to work correctly in your final scene. Now if you are getting into motions and mechanics within 3D you can use basic Euler Angles for simple rotations but if you start to rotate a single object along multiple axes at the same time you will come into problems such as trying to rotate an airplane long both its x and z axis (horizontal) considering y to be vertical you can end up with situations where you will lose a degree of rotation and the freedom of a full dimension as this is called Gimbal Lock. To avoid that we can use Quaternions instead which is very useful and there is an excellent math library that provides all of these operations for you so you don't have to write your own, it's called GLM as it will provide all of the needed vectors, matrices, quaternions and all of the necessary calculations between them including the dot product, cross production, normalization, finding inverses and transpose matrices and much more. But yes; matrices are extremely important in fast and efficient calculations and they are not going away anytime soon. If you have a hard time believing that just watch The Matrix, soon they'll be taking over!

[@darknightninja9773]

skilz8098 Wow, interesting stuff dude! To be honest i dont fully understand the math behind it all, and like you said i use GLM to handle almost everything and treat it sort of like a black box. I understand the significance of mvp ( i dont use the model matrix for my project since i am making a voxel engine and i directly pass the world coordinates into the VS), and the general math behind it but i never really bothered reading its derivation.

[@huverdoose]

Extremely useful for ray tracing as well. ...and visual recognition software. ...and predicting future attacks of Somali pirates. ...and...

[@researchandbuild1751]

Writing a graphics engine from scratch is a waste of your life

[@komodot9249]

Exactly why schools need to teach better at why you are learning something.

[@dineshk9803]

I wished, I watched it before entering into high school, now I'm pursuing engineering. I was like "WOW". Thanks Man

[@sabin97]

yeah. as an engineer i never quite grasped what eigenvector and eigenvalue were......never....until today.

[@dineshk9803]

@Deal Negrasse Bison that too watch it bro 😁

[@minh9545]

Well i was not taught about the use of matrices in high school. Only when we enter university, would we be taught this. I believe this is the perfect moment to know about this as uni is going to start in our country in about 1 to 2 weeks

[@vibinjacob4610]

Spring mass system, Eign Values and Eign Vector kzbin.info/www/bejne/rqunYXepdqeAn7c

[@vibinjacob4610]

@@sabin97 Spring mass system, Eign Values and Eign Vector kzbin.info/www/bejne/rqunYXepdqeAn7c

[@angqingxiong]

1:14 Vectors 4:51 Electronics 5:13 Zombie predict 9:17 website ranking 9:35 assault victim 15:09 Computer graphics

[@BharCode09]

Regarding you recommending 3B1B: Every time a youtuber recommends another youtube channel's video, purely for the sake of it's quality content and not bcz it's sponsored, the humanity is restored!

[@SivaramSarma]

Imma be honest ,u just told me the best explanation for eigen vector and eigen value ,my teacher told me 'just read what's in the book ,u don't need any explanation'😭😑.

[@lunafoxfire]

Same for me! I know a lot about pieces of linear algebra for computer graphics and related things, but still never really understood exactly why eigenvectors were important. Now I have a better grasp on what they actually are!

[@user-lv1wn5wq7n]

I thought that this happened only in Hindia

[@andrewsalazar98]

Should've told your professor, "Excuse me? This class is called 'Linear Algebra with APPLICATIONS.' If you're not going to teach me some applications, then you're just an overrated tutor."

[@ashokjadhav9904]

Ditto here! 😊👍 Most of the maths teacher aren't interested in the subject. Many of them, don't understand it, in the first place. So..... But this guy is great! Not only does he understand, but he has a knack to explain it smoothly.

[@dahawk8574]

Exactly what Ashok said. Teachers dismiss questions because they don't understand the stuff themselves. Like ask anyone why a negative number times a negative number is a positive number. Almost no one can explain it. And this is one of the most basic things we are "taught" in math. The reason why so many students end up hating math is because they have this pile of unanswered questions which eventually becomes so heavy that they end up calling _bullshit._ And they quit. They've checked out. They've had enough. Math is "taught" in a way that is quite similar to religion, in that there are these things that are not logically and rationally explained. The learner reaches a breaking point, and then walks away. The difference is that in math, explanations exist. And the earnest seeker will find the answers, just like MajorPrep found his answers. Well, maybe that isn't exactly a difference. It is said, "seek and you will find."

[@georgecaplin9075]

The times in this video when he said “I haven’t got time to go into it now” or “ this video’s gonna be too long” or whatever, I just wish he’d kept going. I was really enjoying it.

[@anymaths]

watch my helpful maths videos.

[@nourjouini803]

I am studying to become a software engineer and this video has given me the motivation to ace my linear algebra course , I can't stress enough how this video has made me fall in love with what I'm studying and it's applications . This truly has opened my eyes to how amazing and useful the understandding of mathematical concepts is to our lives . Thank you so much for this breathtaking content.

[@Yupppi]

My school's math for matrices had exercises like "this is a table of different product prices in different stores, which store has the most expensive shopping cart and which has the least expensive shopping cart" or "here's a weird shape, these are the corner point coordinates, what's the area" or "this is a list of lab measurements, what's the regression's slope" and all were incredibly easy with matrices and vectors. If my previous school had had these exercises to demonstrate, I'd have never questioned the usefulness. Another thing was in vector analysis getting Archimedes' law, some electric field and other convenient stuff.

[@Cuzilla47]

After almost 53 years, I finally REALLY understand eigenvectors and eigenvalues! I can also declare: "I wish my teachers told me way earlier."

[@Hr1s7i]

Pft some of them probably had no idea what it's practically used for either. If people do internal field research, they don't get invested in the real world. Math as it's own field doesn't really have a purpose other than to teach people how crude virtual logic models function.

[@louisrobitaille5810]

@@Hr1s7i Trying to couple maths and applications is like asking an expert in a field to only teach the basics to beginners for the rest of his life. It's possible, but will be incredibly dull. - The applications of maths is such a tiny tiny tiny TINY fraction of the field that the one doing the teaching will only teach the bare minimum out of boredom while the one learning won't learn anything because the teacher is better at making them sleep than transfering his knowledge. Idk if you got my analogy. I did my best to explain how I see it 😅.

[@w花b]

​@@louisrobitaille5810 maybe but that makes it more engaging to people that don't necessarily see the reason behind learning it. And you talked about math but most people searching for applications are probably in applied math fields like engineering or computer science y'know?

[@theonionpirate1076]

"Any vector that is only scaled by a matrix is called an eigenvector of that matrix. And how much the vector is scaled... is known as the eigenvalue." Wow, those two simple facts would have been nice to have known when I was taking linear algebra.

[@robertcaspari9827]

Right?!?!? Dude i had so many math classes and never really got it this well

[@guitistic]

Exactly. I took engineering mathematics in my 2nd year of engineering and had no idea what eigen vectors or eigen values meant. If only they explained it like this, it would have been easier.

[@IzumuK]

Dude that blew my mind. I had no idea what the heck eigenvector and values even was. I was just blindly calculating them and wondering why the heck I was doing that.

[@alanbouwman5627]

If you paid attention to the definition of eigenvalue and eigenvector this would have been really obvious. In fact, your professor most likely mentioned this while you were not paying attention. Fun fact: "Eigen" translates from german rough as "own" (adjective). But it is just as useful to think of the word own in the verb sense, I think. A matrix (linear transformation) "owns" a vector space when any vector in that vector space stays in the same vector space after that transformation is applied. So saying "eigenvector of a matrix" is similar to saying "the vector owned by a matrix."

[@maxsimes]

Yes this absolutely clicked just because of that

[@mhh5002]

Your and 3b1b ‘s videos are what keeps me motivated for learning math and data science. Thanks and keep up the good work 👍🏻

[@harjotsinghbaidwan2204]

Well said !!

[@haleshs66]

3b1B

[@Blox117]

yeah theres a lot of channels that cover solving math problems but not as many conceptually explaining why and how it works.

[@bithisarkar1412]

What about mathologer?

[@danwroy]

The opening of this video nails it. I didn't understand the point of matrices and when they got to the multiplication system I gave up.

[@maryamali5087]

thank you so so so much, i am a senior in highschoool and i am taking advanced maths, i lmost forgot how passionate i am about maths because how boring our curriculums are, you helped me remember my love for maths again

[@zachstar]

Edit: Made a part 2 to this video! kzbin.info/www/bejne/n2mppp6Bm7J-eas I'm honestly blown away by all the positive comments this video has gotten, so glad you guys enjoyed! I've gotten a lot of people asking for a part 2 so I'll definitely put that on my list of videos to get done. As I mentioned here, the video I did on the PageRank algorithm (kzbin.info/www/bejne/p6monIxuhLiWj7s ) is good follow up if you enjoyed this as it's all about matrices and goes into another application of the eigenvector. It was meant for this video but taken out due to how long it was. I'll work on making a script dedicated to more applications though! In the meantime let me know if there are any other topics you want me to discuss. Laplace transform and z transform videos coming soon!

[@HighestRank]

MajorPrep nix the colloquialisms.

[@borntodoit8744]

I'm about to watch this video purely because i did an Engineering degree which required us to learn matrix algebra. I loved it back then (30 years ago when i was a youngster). It is still all useful and relevant today ...see TensorFlow by Google (re: AI / Machine Learning / Neural Networks training). Maybe you can do a video on TensorFlow too? We referenced 2 Books at degree level (surprisingly well written) for anyone hoping to learn. Google them:- 'Engineering Mathematics' (see ISBN10 # 0333448871) 'Further Engineering Mathematics' by K A Stroud' (see ISBN10 #0333657411).... well worth having as a bookshelf resource. Useful when youre a child learning calculus, as an adult and when your a child again (pensioner) who doesnt want to do Suduko ;-)

[@bk-sl8ee]

U have no idea what u just did there!!! Sir. Our prof. Taught us to find eighen vectors and values but never told what fuck it is!!!

[@henryreese7236]

Hey, while using the zombie example you seemed to imply any vector will be rotated to a eigenvector after successive matrix operations. Is there any result which implies that? I searched for it but couldn't find any.

[@rs45888]

Oh my God.. this is so well explained.. this is the best video I checked on that topic.. i could never really understand this eigen thing until i saw this video.. thank you so much!!!!!

[@Jocularious]

I'm a third year math major. And finally I know what a eigenvalue and eigenvector mean. Like doing the math, no worries. Asking to explain what it is... now that was another problem. Love the channel, keep the hard work up mate

[@Blox117]

"its that thing to do the other thing which gets you the correct answer..."

[@vittoriopiaser9233]

Jordan Turner you should definitely watch 3Blue1Brown playlist “Essence of Linear Algebra”, you’ll love it 👍🏻

[@gflow8357]

You really need to step up your game.

[@anothrto1045]

Ask a stranger what pi is, why it is, and why is it important

[@oliverclennan3449]

G Flow 👎👎👎👎👎

[@douglasstrother6584]

My first exposure to Linear Algebra was a Sophomore course from the Math Department & it was a dry as dust, definition, theorem, proof course. (Granted, I was a 19-year-old at the time!) "Basic Concepts of Linear Algebra" by Isaak & Manougian was the text, which I still have. My second exposure was a year later in a very applied Mathematical Physics course using "Mathematical Methods in the Physical Sciences" by Mary Boas. Approaching Linear Algebra from an applied perspective made it much more interesting and increased my appreciation of the Mathematician's perspective. Linear Algebra is the starting point of learning to visualize higher-dimensional spaces.

[@gracialonignasiver6302]

"There may not be a zombie infestation anytime soon, but this kind of math could be used to analyze how a virus could spread throughout a population, for example." That aged well...

[@meatbleed]

math is only useful with accurate data though

[@jaredgreathouse3672]

No kidding

[@chimero3806]

You could say it aged too well...

[@brendancooney9401]

@@meatbleed LOL, no matter how accurate the data there are plenty of zombies who still dont believe.

[@thanhvinhnguyento7069]

Like fine wine

[@arikayemusic]

YES. I feel like so many courses teach you the computational aspects of linear algebra, but you don't think about what's really going on with it. Amazing vid

[@pspmaster2071]

I took a class called linear algebra with applications....THERE WERE NO APPLICATIONS! Edit: Thanks for all the likes!! Great to know others think the same.

[@iannieves5346]

Try Quantum Computing, a very potentially lucrative application.

[@huey1153]

Ian Nieves he’s not saying LA doesn’t have applications he’s saying they didn’t use any

[@projectjt3149]

Ian Nieves Or parallel programming with GPUs

[@lordx4641]

Typical university education

[@pspmaster2071]

@@lordx4641 I know right. Tell me about it. College is a place to put stuff on a transcript and get credentials. Learning happens outside of class by yourself. Teachers are good to fine tune.

[@ir2001]

Thank you for releasing Season 2 of 3Blue1Brown's essence of linear algebra. His videos included the visualisations of theoretical concepts and yours showcase the wonderful applications of matrices!

[@randomdude9135]

He should make a series on Group theory.

[@randomdude9135]

Like the one by Socratica.

[@randomdude9135]

Or Ring theory.

[@mayankraj2294]

.

[@mayankraj2294]

.

[@mra1685]

I never thought i would be this happy about understanding something i have learned without actually understanding it. Thank you for the taking the time to make such great videos. i think i found my new favorite channel :) .)

[@andrewgjennings]

Suddenly, matrices aren't so scary. Thank you for putting this video together. As a computer programmer, we deal with this all the time. Because we don't call them matrices - we might call them something different, like tables, arrays, grids, etc - I got the idea that they are completely different disciplines, but you just proved they aren't. Spectacular video and explanation. I wish I'd known this decades ago. Well done!!

[@RunOs3]

This is by far the best explanation I have ever had in my entire career as a math student.

[@primajump]

This is one of the best presentations that help to appreciate the value of matrices. The simple explanation of eigen vectors and eigen values was just brilliant. The speed was just prefect that I did not need to go back and forth. Thanks for posting this.

[@KeithRowley418]

best introduction to matrices I have ever seen. This sould have given me so much more initial insight an understanding when I was learning engineering math!

[@BangMaster96]

OMG.... I just took a course on Linear Algebra and Differential Equations, the whole time, i never understood what the hell are Eigenvectors and Eingenvalues, i just did the calculations using the given steps and formula, but never knew what it meant. Finally, all the dots are connected, it makes so much sense now. Thank You MajorPrep, this was so good and interesting to learn.

[@justingolden21]

Zach: "There may not be a zombie infestation any time soon" 2020: "Don't test me child"

[@danpal6737]

nah its almost over 2020

[@betterfly7398]

@@danpal6737 2019 was almost over when COVID-19 appeared.

[@rthelionheart]

Linear Algebra is by far one of my favorite classes taken as an undergraduate student. Very interesting class.

[@oh-yt9ug]

I was having flashbacks to my linear algebra class watching this video

[@earavichandran]

All my expression, reaction etc after watching this video is AWESOME. Unbelievable explanation. Hats off to you. I am now your big fan.

[@RecursiveTriforce]

22:50 To those who want to know how the "divide by 6" was derived: As he said the Trace(A³) is just how many paths are between a person and themselves. But this little triangle can be walked through... 1. clock- and counterclockwise (2 Options) 2. starting from every vertex (3 Options) So you will count every triangle 6 times.

[@jonnamechange6854]

What's the point of this? Is it for setting up a ménage a trois, or some such group sex?

[@zachstar]

@@jonnamechange6854 Yeah in the dating app case it tells you how many genuine 'love triangles' or potential threesomes there are where everyone is happy.

[@jonnamechange6854]

Well done for making mathematics sexy. When I started learning matrices we didn't have the internet or advanced computers, so all these applications had not yet been created. I always asked the teacher what application there could be but he told me not to ask. Everything on the subject's syllabus had to be known and committed to memory without even the slightest explanation as to why.

[@goosecouple]

Doing things = Operation

[@nel_tu_]

The formula for squares is wrong. idk how you arrived at it.

[@prabhatchanchal]

"As much as I’d love to keep going into depth on different subjects, this video is already quite long.” Sir ,It doesn't matter how much long the video. I can watch your video entire day long. please keep it.....

[@eleazararce5716]

When I got to time 4:20 I had to pause and recognize that this video has been more insightful than any other resources I've used to understand these concepts. I'm currently registered to take this class after many year of going through it. This time it will be more enjoyable! Please keep making great video like this!!!

[@000998poi]

You're a saint for explaining things so transparently and for giving real world case scenarios.

[@aman2426]

This blew my mind. I have a recommendation that you should have given a short summary of the video at the end. That would have made it more effective.

[@rameji-chan737]

Eigenvalue and Eigenvector both have the german word "eigen" in them, meaning "own". So "Eigenvector" means "A vector owned by the matrix". Makes it easier for me to remember what these two things are doing.

[@JonathanMandrake]

Yeah, as a german, these two words made much more sense when learning about them

[@WatDoino]

Man I hated those terms in my class. I understood absolutely nothing about any eigen crap. I also had a russian math teacher whose voice made me so sleepy.

[@fernandomoraescrescencio6428]

in Portuguese their called "autovetores" auto -own vetores -vectors

[@statisticallylaura]

Gosh, even as a German with that understanding, it took me a while to grasp their full meaning. Cannot imagine how abstract it must be to not know that from the start - never occurred to me that not every teacher brings this up immediately.

[@JohnAlanWoods]

Super vid. After 4 years of engineering I didn’t understand Eigenvectors. 20 seconds here I do. 👍🏽

[@otrrsuns3t]

This was assigned to be watched in my University class. Writing a test tomorrow, might as well procrastinate productively ;)

[@redarmy724]

I don't know why our teachers and professors at school never shown me this. All I know is this video must have helped millions of linear algebra students to do better and pass the class. I have been stressed out with linear transformation for weeks. This video has helped me visualize everything in a simple and logical way.

[@harshsharma5768]

Linear algebra came in my 2nd semester electrical engineering and i used to calculate eigenvalues and eigenvectors of matrix blindly without knowing why am i doing it. Now i came to know what they really mean and why do we get infinite number of eigenvectors for a particular eigenvalue. Please make more videos on these kinda stuff!😃

[@souravpaul2179]

Msc paas kar liya kab ka mujhe toh aaj bhi samajh nahi aaya...shaabash

[@abeluchuya5547]

I study fluid/structure mechanics and I swear matrices are everything!!

[@tuskofgothos2637]

I absolutely love this video, and I am only halfway through! I have a fear of maths, but videos like yours give mathematical concepts much needed context and take the edge off that fear.

[@LorenaGonzalez-fr1fm]

The first 5 minutes helped me to definitely understand what I’ve been doing for years without knowing the reason why. Big thanks!

[@johnquinn6]

Zach, I am coming to the end of year 2 of my undergraduate degree in mathematics. In year 1 we did linear algebra and covered eigenvectors and eigenvalues, and in year two we are using said linear algebra in computational mathematics. I have paused this video less than 3 minutes in so I can leave this comment. In less than 3 minutes, you have explained more about the role of matrices, and more importantly, what eigenvectors and eigenvalues actually are. It is absolutely astonishing that I am paying so much money for an undergraduate course when there is better tuition to be had on youtube. I appreciate this video and I have subscribed to you channel.

[@InstrumentalAvenue]

Eigen see clearly now the rain has gooonnnne.

[@Y45HV1N]

as a non mathematician who has been struggling to understand matrices, this has helped a lot ! thanks!!

[@randomdude9135]

This was the fastest 12mins 47.5 secs in my life so far. Interesting video. This channel is pure gold.

[@kentlab3850]

I think you meant 12min37.5sec

[@randomdude9135]

@@kentlab3850 No. I had to rewind some parts so they took some extra time.

[@C.K.Productions]

I often feel very insecure about my math. My school district wasn’t the best, and by the time I got to high school everybody was trying to introduce common core but my teachers wouldn’t abide by the curriculum. Half the time they wouldn’t even show up. I remember I understood absolutely nothing on the math portion of the ACT. I’m almost done with my undergrad degree but math still haunts me. I still feel very inferior. Thank you for your videos

[@Robin.Hollinger85]

No teacher ever told me what this was used for in grade school, and it drove me nuts back then. Just today it popped back into my head and I googled it. Thank you!

[@alexlemarchant4376]

About a week ago I asked my teacher this exact question and she just brushed over it thank you

[@douglasgorden3843]

I love the zombie example. I'm going to use that in my chemistry classes to introduce the topic of equilibrium.

[@thatguyben7754]

I knew a good amount of this, but that one about the dating site was really cool and interesting. It’s one of those things if I know where they’re used, just not how

[@brunojani7968]

I share this opinion. I knew about adjecency matrices and A^k showed me the nr of paths of length k. But the application in terms of the dating app was a real treat.

[@simonnordon8421]

best video I've seen on matrices in 10 years. thank you.

[@ABSP5766]

Thank you. I am taking a course on Linear Algebra and I really couldn't make any sense of what I am learning there. This video has been more helpful than many hours of study there, because now at least some things start to click.

[@zeeehnbugattiisyeah8294]

I've been following this channel for a while now and I just wanted to give a huge thank you for raising my interest in math and its apllications even more and more! I'm starting university next week and you just motivated me so much for my linear algebra class. Greetings from Germany ;)

[@kmax3339]

I wish this channel existed during my student years. It really would have made a difference.

[@becomepostal]

I’m not sure it’s enough.

[@chintakgurjar8426]

I have taught these mathematical topics to students in college. You gave me new insight. Thank you 🙏

[@srikuhere]

wow, this is how education should fell like . learnt matrices in school , did well in the exam however stayed matrices ignorant , now i am educated in matrices . your video will help me in my data science education . thanks man

[@claudioamorim9268]

Congratulations for conveying a seemingly dull subject into a shinning video.

[@itsrandeep]

If we had more teachers like him... The world would be different!!

[@preetammeena593]

We now have and just need to search the internet, where as it was really hard to find good teachers prior to the internet.

[@retiredmeme2751]

that was the most easiest-to-understand definition of eigenvactors/values that no other resource could provide

[@hrivera4201]

This one is equal or better: kzbin.info/aero/PLZHQObOWTQDPD3MizzM2xVFitgF8hE_ab

[@genecat]

When they start giving awards to KZbin videos, this one is sure to be a winner.

[@edwardwong654]

I remember in the movie, "No Way Out", with Kevin Costner, he is a naval officer who works for the Secretary of Defence, Brice (played by Gene Hackman). Both of them are an affair with Sean Young, who was killed by Brice when he became enraged at her. Brice then works on a coverup to protect his powerful position, at which time they find an indiscernible negative of Costner in Young's residence. Brice decides to use the negative as a phony coverup that it was the spy, "Yuri" who had killed Young. Brice asks, who else of course, but Costner, to handle the of enhancing the Yuri negative in order to create a red herring to hide his involvement in the death of Young. Costner has no choice but to handle the enhancing, by giving it to an expert, who uses a process with Eigenvalues, to start the intensive enhancement process. But I never forgot the use of Egienvalues from that movie. That was actually a pretty good movie. Spoiler alert - turns out that Costner, by coincidence, was actually the double agent, Yuri. Also the DC Metro scenes were filmed in Baltimore, and not in DC.

[@utkarshupadhyaya7091]

I recently started working on photoshop....n was wondering hw the hell they have advanced the software to this level. Now i know....thnx 👍 i love maths ❤️

[@DMGGoodTimes]

youtube pls recommend this video to Indian students 🙏, they need to see practical uses other than just theory

[@jasminemallick1215]

An Indian student just saw this

[@GuilhermeDiGiorgi]

This reminds me of another video where it was explained that they used multiple sine functions to create an image. Mainly to store finger print data in a more compact way

[@Rudxain]

JPEG uses the Discrete Cosine Transform to compress natural photographic data. IIRC, PNG also does the same but in a lossless manner

[@parrotraiser6541]

The one thing that is missing from all the "Introduction to Matrices" that I've tried to follow is a simple. real world example to use as a mnemonic and check for basic operations. Converting a realistic example to matrix form would ground it in memory, and knowing the answer would serve as check when calculating.

[@sgringo]

That was a great explanation. I learned about matrices in a university finite math course. I learned the material, but like you said, I was left with absolutely no context for how/when/why to use them. I acquired that context a few semesters later, during a computer graphics course assignment to create a "spaceship" (really just a simple triangle with three vertices) that flew in a large circle on the screen. The challenge was to ensure that, as the ship moved around the circle, it reoriented itself correctly, to always be pointing in the direction of travel. This was accomplished by multiplying x,y for the three vertices through a hardcoded 2x2 matrix to get the next set. (The matrix was more complex than the example you provided; it utilized trigonometric functions). That assignment was the only context I ever had for matrix operations... until now! 👍

[@Kitten_Stomper]

This video just explained with crystal clarity what an eigenvalue was. Back when I took linear algebra, one if the things that baffled me was what an eigenvalue was.

[@pendragon7600]

Matrices are not boring at all

[@jonathangomez9901]

Like the name

[@huey1153]

Yikes

[@lordx4641]

Exactly its easy and kogicak with less knowledge as it plays with combinations. Jist imaging if we were learning math from practical examples. Thats why ppl like physics more than math because they know the analogy

[@seeklampton9031]

It is easy more than set and function. I like plus, times,inverse, determination of Matrice.

[@SirMathBoi]

True...very true

[@zoltankurti]

Stress forces and deformations of solids are also described by matrices, and in quantum mechanics all observable quantities are associated with infinite by infinite matrices.

[@la6beats]

"Could be used for a national virus outbreak or something but that will not happen" Well.... 👀 at least i can use the shitty math they taught me back then now in real life

[@FalconX88]

And hey, now we got riots in LA too. This video really predicts the future.

[@joelcoll4034]

@@FalconX88 I was thinking the same 😂😂 I actually thought this was a very recent video until I checked

[@hassanyare9963]

i am planning to take a new course on image processing an this helped me a lot thank you so much for all these quality videos

[@abhishekpa2088]

Amazing... My interest towards linear Algebra is now more.. Thanks to you.... Wish my teachers taught this way...

[@rjk0128]

Wow this made me pumped to learn more Linear Algebra, much appreciated!

[@roygalaasen]

When I saw that 20% of humans turns to zombies, and 10% of zombies turn to humans, I thought to myself that it couldn’t be so simple as to be twice as many zombies as humans. Alas... (This is a great repetition video on linear algebra!)

[@alexanderdanko9062]

"but this kind of math could be useful to analyze how a virus throughout a population" he tried to help.....

[@ailecdreifuss8627]

Yes it can, is used in health economist and epidemiology "Markov model", but of course is little more complicated since one have to add certain variables.

[@georgesbegon4252]

Je me méfie des affirmations extensives et péremptoires basées sur de l irrationnel, serait il viral

[@ViratKohli-jj3wj]

@@georgesbegon4252 चुप गधे

[@danpal6737]

aqui sigo sin infectarme , cuando la vacuna prroz.

[@heyman9078]

@@georgesbegon4252 🤣🤣🤣merde gars de quoi tu parles?? We don't catch you anymore!

[@TheOzpad]

No, Zach I want to learn MORE about how matrices are used so please do a longer video! The network and image processing examples BLEW MY MIND

[@hurlprasad]

I never understood the importance of Matrices, though I was very good at solving Eigen Matrix, determinants, etc. I don't know whether I have typed the name correctly or not, but thanks to Zach, now I am going to know the applications of Matrix... Thanks for helping us fools to understand the beauty of Mathematics... 🙏🙏

[@Vyantri]

If I was a lecturer, I would play this video for my students during their first linear algebra class.

[@seeking9145]

Fun fact: I'm a german and everytime I am surprised because Eigenvector and Eigenvalue (or in german Eigenvektor and Eigenwert) are international used declarations. In german "eigen" means something like: "mine" or "belongs to me". There is no corresponding word in english, which may cause that american scientiest take over the same name from the german mathematics. So in german it is a very matching name, because the Eigenvector and Eigenvalue belongs to exactly this one matrix.

[@Primitarian]

I think the English equivalents would be "own" or "peculiar"--"peculiar" in the sense that it is the only one of a thing.

[@krzysztofwojda9179]

@@Primitarian Probably their discoverer was german, and in translation it's been taken into account. I'm Polish and the word used to label them has the same meaning. We call the eigenvector ”wektor własny”. And Krzysztof is polish Christopher ;)

[@Primitarian]

@@krzysztofwojda9179 And my last name is Julka, which I'm told is Polish (or possibly Czech) for "Julia."

[@krzysztofwojda9179]

@@Primitarian I'm not sure if Czech version isn't "Yulia", but you're right, Julia is a women name in Poland and Julka is its colloquial version. Poles could have a problem figuring out which is your first and a last name :)

[@Primitarian]

@@krzysztofwojda9179 So it sounds like "Julka" is not a common last name, even in Poland. Interesting in any case, thanks!

[@SachinKumar-de8nd]

For the first time i saw a 25 min video without even skipping a sec ,and also I was so into it ,basically completely lost

[@stephenholland6328]

This is the first time anyone has succinctly explained what eigenvectors and eigenvalues are!

[@cinnamonbun5530]

Can't believe you made me listen to matrices for a whole 25 mins and I didnt even notice its that long until you said so..😍😍😍 who knew math was fun. I'm pretty sure even my math teacher didn't know this

[@divyanshukumar813]

I learned here much more than I learned my whole school and university life. Great Video!!

[@blzKrg]

One of the most interesting math vids on the internet.

[@arpanchatterjee2596]

Glad someone made this stuff, the title too included in the delight.

[@edykadosh2558]

My university teacher recommended this video to the entire course. Thank you for making such a great video!

[@esPeSkull12]

Please keep doing these kinds of videos! I remember doing highschool math and coming across your "common math mistakes students make", which helped greatly. I'm doing Linear algebra atm and this makes a lot more sense than trying to keep with the 300% speed trail of thought that my teacher has.