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

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.

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

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.

yessss

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

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

Lolol

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

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

Bow chicka wa wa

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.

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

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

@@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?

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!!

math is only useful with accurate data though

No kidding

You could say it aged too well...

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

Like fine wine

This is even more important in the age of internet where information is out there open for everyone to access freely. If one knows why something is important, then it'll be easy to teach oneself. The role of the teacher is therefore to guide the pupil on what is important and why.

I think they often don't really know themselves - I mean they're teaching not doing robotics. They need to get people like you to come and explain the whys.

To be fair, the applications are so wide that it's very difficult to even begin to describe what they can do. I didn't understand their geometric interpretation despite reading about them a several dozen times. Even now, there are still things that I'm learning about them.

No Shit!

Totally agree. I saw no point in all this "garbage" only when I started to work and I have seen what this is used for it made sense and is actually interesting and easier to understand, now trying to catch up. Education systems are so broken, they cannot keep up with what is happening and why it is happening.

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.

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

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)

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

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.

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

@Deal Negrasse Bison that too watch it bro 😁

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

Spring mass system, Eign Values and Eign Vector ru-vid.com/video/%D0%B2%D0%B8%D0%B4%D0%B5%D0%BE-xzD0DsABMiU.html

@@sabin97 Spring mass system, Eign Values and Eign Vector ru-vid.com/video/%D0%B2%D0%B8%D0%B4%D0%B5%D0%BE-xzD0DsABMiU.html

nah its almost over 2020

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

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.

@@randomrandom316 Can't agree more

ESPECIALLY IN INDIA

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).

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.

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.

@@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.

@@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

@@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.

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.

3blue1brown makes much better visual explanations.

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

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

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

I know, he's a prophet or something

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

THIS!!!

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!!!!)

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

i m from India

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

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

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!

Trinidad

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.

@@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 😅.

​@@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?

LSA? You’re the man

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.

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

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.

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.

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."

Yes this absolutely clicked just because of that

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!

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.

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

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

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

Try Quantum Computing, a very potentially lucrative application.

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

Ian Nieves Or parallel programming with GPUs

Typical university education

@@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.

Well said !!

3b1B

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

What about mathologer?

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!

I thought that this happened only in Hindia

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."

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.

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."

watch my helpful maths videos.

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

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

You really need to step up your game.

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

G Flow 👎👎👎👎👎

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

He should make a series on Group theory.

Like the one by Socratica.

Or Ring theory.

.

.

MajorPrep nix the colloquialisms.

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 ;-)

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!!!

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.

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!!!!!

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

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.

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

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.

Like the name

Yikes

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

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

True...very true

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.

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

@@georgesbegon4252 चुप गधे

aqui sigo sin infectarme , cuando la vacuna prroz.

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

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

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

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

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.

Doing things = Operation

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

I think you meant 12min37.5sec

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

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.

This one is equal or better: ru-vid.com/group/PLZHQObOWTQDPD3MizzM2xVFitgF8hE_ab

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

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

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