This was filmed in 2005 when Gil was 70. He just retired from MIT this month (May 2023) at age 88 after a 62 year career as a professor. What a great career.
@@henryfordsonofindia8399 Yeah, he seems to be in very good shape for his age; he can walk around in front of the board, and he can juggle around matrix algebra with ease.
I wish I had teachers like Prof Gilbert Strang when I studied linear algebra. What a difference makes to have someone dedicated to explaining the geometry of what is going on.
33 years ago I was told to read his book on linear algebra and its applications, my first experience of learning this stuff...did not always work for me, but I persevered with his approach and got there in the end. It's amazing now to see what he actually looks like.
00:00 Course overview 01:00 Lecture overview 04:25 Row picture 2D 08:35 Column picture 2D 15:38 Row Picture 3D 22:00 Column Picture 3D 27:55 Can I solve Ax=b for all b? 32:25 "Visualise" 9-dimension 35:33 How to multiply a matrix and a vector?
We're using Professor Strang's book in my linear algebra class and I really cannot understand my professor's teaching style. My friend pointed me to these lectures instead and I already feel like I actually understand a lot more from this one lecture than I have the past two weeks in my class. Thanks Professor Strang!
Hmm...I wouldnt go that far. Imho, he is a good teacher from what I've seen here. He clearly cares about teaching, and he engages his students the way a good teacher should. He starts from first principles and assumes next to nothing about his students. But I wouldn't call it artistry or a masterpiece of teaching haha.
Yes... it's interesting how you can't really just rely on a book, and why it helps to watch a person actually doing it. And the style totally is important.
An amazing first lecture, glad to see the audio is fixed, thanks for taking care of this course. It's beautiful to perceive people from all over the world gathering here to gain knowledge, Professor Strang is a great teacher
For everyone begining this lectures that have no notions of linear algebra, I reccomend you to watch 3Blue1Brown series before because he put a lot of image on the word. Sorry for the mistakes, I am not an english speaker.
@Chris Metcalf i got my eyes on landing a job in data science for myself, just brushing up the mathematics behind machine learning but definitely not planning on doing deep theoretical tinkering and what not
Hi professor and online collegueas. I'm a control engineering student, so Linear Algebra is the essential of my field of study. Despite I've taken a linear algebra course before and even sophisticated discussions in control systems, I never truly understood until now why it is better to think using columns instead of using rows. But now it's totally clear in my mind, so thank you very much, professor Gilbert. I'm anxious for the next classes.
Please spread this school on your wall and your friends because students need to see it. So will you. There are more than 4 000 tasks and theorems for primary and secondary school students. Thank you for your contribution. Respect! ........................................... .Të lutem shpërndaje këtë shkollë në murin tuaj dhe miqve tuaj, sepse nxënësit kanë nevojë ta shohin. Kështu do të kontribosh edhe ti. Janë më tepër se 4 000 detyra e teorema për nxënës të shkollave të nivelit fillor dhe të mesëm. Faleminderit për kontributin tuaj. Respekt! ruclips.net/channel/UCELXh5_dCYX6umKP3qlOL9g
That makes me remember the first semester linear algebra lecture. He certainly takes his time to explain, what the interpretation is and that is wonderful. We were not so lucky unfortunately.
Gracias Dr .Strang ,yo estudie algebra lineal con su libro ,pero verlo a Ud ,explicando en ingles , me llena de emoción , desearóa estar en su clase ,es un genio ,en persona es mas de lo que pueda decir su libro ,Mi admiración y respeto , Que calidad magistral para explicar algo tan ABstracto ,lo hace ver facil y sencillo,tanto que hasta mi hija de 12 años que esta en primaria lo entiende ,es un superhiperExplicador
@@bouthaina7846 hi can you tell me what is the application of Linear Algebra in ML ? I really confiused whit vector space and Scalar field and what we exactly model and do in linear algebra
@@rezaadventures actually I'm so new and just started studying machine learning but for what I've seen in neural networks, PCA and a lot more things everything is about matrices and linear algebra so I've decided to firstly understand linear algebra then everything else will be quite easy ...
as a 1st year grad student a very long time ago, i took a course in linear algebra using Gil Strang's book. learning about the relationship between the four fundamental spaces of a matrix felt revelatory at the time, and i still have that book. he's such a wonderful expositor.
This makes me want to applaud. I watched his summary lecture that reiewed this course and I damn near clapped in my home. I should buy his book - I bought another one that's working fine, but didn't emphasize the row space column space null space left null space fundamental theorem of linear algebra picture that this course develops.
❤0:54 the fundamental problem of linear algebra - a system of linear equations needs to be solved 1:13 1:25 ❤1:49 "picture a column at a time" 2:02 2:12 2:59 3:10 3:34 3:40 A is the matrix of coefficients 5:57 6:23 The line of solutions to this equation 8:34 14:13 23:44 26:00 big picture 29:30 multiplying a matrix by a vector. AX
Prof Strang really LOVES teaching, his soul is part of it-they say a genius make poor teachers- he is the one exception- Thank you for your efforts to bring people into your world
SO fantastic！！！THE Right way to open Linear Algebra!!! 我是来自中国的学生，当我认真学习线性代数的第一堂课后，我被深深的shocked到了！让我重新理解了维度！ N-D space is a combination of N-1-D sapce and non-N-1-D vector!
guys if you are here because of machine learning then trust me this course is the most most useful one to do before even starting machine learning i can ensue you it worth it 100% i myself have completed this series and it just gave me leg up in ML trust me after this course you will be able to understand ml concept that some of highly paid ML people can't! it will be such a leg up in you ml career i swear i wish i can erase it from my memory and do all it all over again p.s please do it right tho understand every concept go through book and do exercise if needed give it good 3 months atleast
Soy arquitecto, antes de ingresar a la facultad ingresé también a matemática pura, lamentablemente dejé las matematica por la arquitecturas, ahora devoro libros de matemáticas, espero algun dia retomar mi camino, mientras tanto me divierto con sus clases....y la pasión aumenta. Saludos!
I always dreamed (and still continue) about studying at MIT, but I am not a genius and not a daughter of some deputy, so instead of university lectures I watch this course and imagine myself studying there))
Luciano Rodriguez this is true. I attend an Ivy League university and paradoxically, the intro level math classes are awful, I study from MIT materials
I mean you also have to think about the school fees and see if it's worth it. I don't think it's as black and white as you may think, it's probably more grey.
thank you Mr Strang for your lecture!!! i don't understand yet the fact that with 2 millions subscribers, only 4000 folow your lecture!! Your chain is one of the best i found regarding basical science, congratulations!!!
In the first lecture, from 14:10 to 15:26 the dude threw on the gem. If you notice this is the idea of vector spaces something which really you don't understand when you start linear algebra. Moreover, he pushed the argument at 22:00 with all the beauty to show that a column picture is a preferred way of looking when it goes into a higher dimension, the point on which he comes back in vector spaces. Finally, at 28:00 he concludes an important thesis for vector spaces.
This might help others trying to learn this material. I found it easiest to watch a few lectures, but without being overly concern about learning exactly whats going on. This gives you a basis to work from. Then get the text book and work though it slowly. Write down the examples in the book as you encounter them and get used to forming a mental picture for whats going on. The column picture is key. The row picture is probably what your school math teacher taught you. This just confused me a lot. I don't like dot products, but the "combinations of columns" is very intuitive once you can visualize why it works. The reason I found this easier is that the concepts introduced in the videos are a bit loose, its just an overview. The real learning comes from the text book.
I had linear algebra over 40 years ago, but this was the first time I'd seen it presented this way. I've done fine in my engineering career, but this kind of thinking would have definitely made a few things easier.
I'm a student in Ariel University at Israel. I'm studying computer science and math, and I just want to say that you are a terrific teacher! I will recommend your lectures to my friends for sure! Thank you a lot.
10 years ago I skipped Lin Algebra class and learned by watching this fantastic series of lectures. Moved to have learned that Prof Strang just retired. A big thank you to him for delivering such well thought through and well paced lectures.
I'm really happy that great lectures are available for free. Young people should appreciate it that they have internet and they can learn from materials from other universities especially from other countries from another part of the globe.
One of the best teachers! As a viewer of this course you feel the passion and love for math. He feels the math and can transfer his knowledge to other people. Well explained! Top!
Even though I've learned Linalg from my undergraduate course, it was ages ago. Thanks to Prof Strang, the explanation of the geometry meaning of the matrix is much clearer than what I've ever been given.
You know a man's the GOAT if lectures from almost 2 decades ago with chalk and a blackboard are better than 90% of the content online. Thank You, Professor Strang and MIT for bringing such amazing content to the world...
When we get linear equations, Ax=b, where A is an n x n matrix, and x and b are column vectors with n components, we can see b as the linear combination of column vectors of A and components of x is equals to b. That is, column 1 of A * 1st component of x + column 2 of A * 2nd component of x ... + column n of A * nth component of x. This view is new for me. Thank you, Prof. Strang.
Why is Prof. Strang so successful at teaching? It's not just that his explanations are clear and reasonable. His personal style has a lot to do with it. He comes across as unpretentious and as someone who is doing this journey with you.
I can see in the class of this excellent professor and mathematician what the real problem in mathematical education is: our obsession to cover the topics always skips the necessity of the students to form the proper intuition of a topic. Intuition takes time, but above all takes proper activities to develop it. His talk is basically about the generation of spaces through linear combinations, but honestly could anyone sitting down there and listening reproduce those ideas without the help of proper representations, say, software, or at least good pictures? In mathematics, physics etc, intuition is the most important, but scholastic education has always tortured them with logic. That is totally unfair and a waste of talented students.
Why u say it is devoid of intuition when he is showing exact steps of logic? Sure, u may miss understanding the steps of logic, but nothing he is saying depends on intuition! Follow the formula correctly, get the right answer! Make a mistake in calculating, get the wrong answer!
24:44 thanks to prof. strang that he didn't get away by just taking an easy example and explained other cases where it didn't work. . . . 32:20 the way professor strang visualise the 9 dimensions is so impressive
Linear Algebra runs in his blood (Prof. Gilbert Strang). I now understand Linea Algebra thanks to his amazing lectures and his too much insight into this subject!!! He opens mind and unlocks concepts which are not naturally easy to grasp.
My lecturer in Linear Algebra was pretty good at doing mathematics but he was not so good at explaining it. I have really enjoyed these lectures and came back to the start just to encourage others to watch and enjoy.
thats the greatest explanation of geometry of linear equations i have ever seen, thank you for everything sir, greetings from istanbul technical university
The only disappointment for me is the fact that Prof. Strang can't see my submission to his excellence and gratitude for his contribution, as I feel every time I see him.
🎯 Key Takeaways for quick navigation: 00:55 🎓 *The first lecture of MIT's linear algebra course focuses on solving systems of linear equations.* 04:08 📊 *Linear equations are represented as Ax=b, where A is the coefficient matrix, x is the vector of unknowns, and b is the right-hand side vector.* 08:47 🖼️ *The column picture of linear equations involves finding linear combinations of column vectors of the coefficient matrix to produce the right-hand side vector.* 14:59 💡 *All possible linear combinations of column vectors fill the entire space of achievable right-hand side vectors.* 20:58 📐 *In three dimensions, the row picture of linear equations involves planes, where the intersection of these planes represents the solution.* 25:39 🧠 *Lecture on elimination methods for solving linear equations is upcoming, crucial for software and production applications.* 26:38 🔄 *Changing the right-hand side of linear equations can produce unique solutions, impacting both row and column perspectives.* 28:31 ❓ *Can the linear combinations of matrix columns fill three-dimensional space? Answering this question is crucial for solving equations for every right-hand side.* 31:40 ❌ *If matrix columns lie in the same plane, the matrix is singular, and not all right-hand sides have solutions.* 33:32 🌌 *Understanding linear combinations of vectors in higher dimensions is essential for grasping linear algebra concepts.* 35:45 🔄 *Matrix form of equations, A*x=b, highlights the importance of matrix-vector multiplication, viewing it as combinations of matrix columns.* Made with HARPA AI
Comman man's Justice League:- Batman, Superman, Wonderwoman, Aquaman My Justice League:- Gilbert Strang, Walter Lewin, Ben Polak, Patrick JMT, Ben Lambert
attend to the strang paradox; a vector field of unfinished sentences that form the basis vectors for a stunning range of interesting algebraic problems
Thank you Dr. Gilbert Strang. I am a senior lecturer at Azerbaijan State Agrarian University. I teach the subject Linear Algebrain in English . You explain very clearly.
I enjoyed this lecture. Professor Strang seems like a congenial person truly interested in imparting his knowledge. Some professors seem to look down on their students and have the attitude that if you don't get it, tough.
Really got the points! First time in my life I have completed a lecture on math and also learned multiple new things! All concepts got cleared. Thank you Gilbert Strang for introducing me to LA. Respect++;
Amazing! I like linear algebra a lot, I already had this class in college, I keep reading about it and ... I didn't even notice the passing of 40 minutes of the first class you! No wonder MIT is a world reference!
My term 2 (semester 2) is about to start. There we have maths 2 and to prepare myself for that I am here.My Senior suggested me this. I am in foundation level (1st year) of IIT MADRAS (India) BS in Data Science and Applications. Seems good one! Yet to explore more! By the way Thanks to Respected Prof Gilbert and MIT.
In my whole life never did this matrix multiplication make me sense like why are we doing multiplication and addition to numbers in a box in a specific manner, which is very non-intuitive, But the column picture idea that you gave makes me think it is matrix is an awesome tool to the equations
Linear Algebra has been my good old friend for several decades, but now I see a fresh look at my friend that looks much younger, all this thanks to the amazing profession Prof. Dr. Gilbert Strang. The essence of the timeless reverence Guru Brahma proved again. I shall be going through the entire series, even though, I wish I had this opportunity a decade and half ago. 🙏
I olny had math until 6th form (around 12th grade) and i was invited one day to see a matrix class. And let me tell after the first 14 minutes of this video i really felt in love with maths
It's such a privilege to watch this honourable man delivering a lecture. Your lectures are helpful, especially, to the people living in a conflict zone like Kashmir, where the lockdown extends for months and this time it is almost a year with the continuous lockdown. Your 39 minutes lecture takes us more than 60 minutes to stream because of 10 months long high-speed internet restrictions enforced on us by the government's fascist approach. We have to make do with whatever we can with 2G networks. The board appears blurry because of slow networks. Thank you, sir. Thank you, MIT. Thank you, America. ❤
I have always preferred solving linear equations with matrices, it is my go-to method. I like it because it is faster, saves me from having to write all the variables at each step, and because it is so neat and compact makes it easier to find errors. 5:00 It's always easier to rearrange the equations to the point-slope form which makes plotting so much easier. y = 2x, and y = x/2 + 3/2. 13:00 It would be more helpful to draw the resultant vector, (0,3) first so the target is plainly visible.
"It's the right place to start".. now, ..continuous observation of logarithmic 0-1-2-ness Polar-Cartesian i-reflection z axis containment in/of the x-y plane vector-value, convergent con-sequence, positioning. This is the "long hand" breakdown of pure-math Actuality, point-line-circle log-antilog conic-cyclonic coherence-cohesion Timing-Spacing.
I passed my linear algebra with a 100%but I literally didn’t know shit why those are happening. Thank you Dr Strang for letting us know what is linear algebra truly about.
![Noob To Max With DRAGON REWORK In Blox Fruits [FULL MOVIE]](http://i.ytimg.com/vi/LnBMOinoOvA/mqdefault.jpg)
Audio channels fixed!
Awesome! :D
God Bless You, MiT and Gilbert Strang! You deserve a lot of praise for this series, now in even better quality.
Thank you MIT OpencourseWare
Mit please provide a series on propositional logic and predicate calculus.
Many thanks to MIT and Professor Strang! We love your work
This was filmed in 2005 when Gil was 70. He just retired from MIT this month (May 2023) at age 88 after a 62 year career as a professor. What a great career.
Wow, he looks so much younger than 70 in this lecture
@@mgh7818
I would have guessed maybe 55-60.
Was he 70? And retired at 88 this year 😲😲😲
@@henryfordsonofindia8399
Yeah, he seems to be in very good shape for his age;
he can walk around in front of the board, and he can juggle around matrix algebra with ease.
Fastest moving, smartest 70 year old, prolly ever.
In two years of junior college and 4 years of engineering, not once did anyone gave the column picture explanation. Mind blown. Thank you, Dr. Strang.
I wish I had teachers like Prof Gilbert Strang when I studied linear algebra. What a difference makes to have someone dedicated to explaining the geometry of what is going on.
33 years ago I was told to read his book on linear algebra and its applications, my first experience of learning this stuff...did not always work for me, but I persevered with his approach and got there in the end. It's amazing now to see what he actually looks like.
Lies again? Gay Of LA
I took this class from him in the 1980s. He was a great instructor.
Thank you Dr. Strang. I graduated from high school functionally illiterate in math. In my journey to teach myself math you have become a great mentor.
I second this! I was exactly the same!
Me too! Here on Mars good math professors are a scarce resource too!
Good luck!
Good luck in your amazing journey
@@georgecarlin2656 uhm...MARS????
00:00 Course overview
01:00 Lecture overview
04:25 Row picture 2D
08:35 Column picture 2D
15:38 Row Picture 3D
22:00 Column Picture 3D
27:55 Can I solve Ax=b for all b?
32:25 "Visualise" 9-dimension
35:33 How to multiply a matrix and a vector?
@MIT OpenCourseWare please copy this info to the video description so it becomes visible in the video timeline
Someone do this for every lecture video
Took 18.06 in 1992 and he taught it. Great stuff, and an awesome professor.
We're using Professor Strang's book in my linear algebra class and I really cannot understand my professor's teaching style. My friend pointed me to these lectures instead and I already feel like I actually understand a lot more from this one lecture than I have the past two weeks in my class. Thanks Professor Strang!
Professor strang is master of teaching
He is an artist.
His way of teaching is a masterpiece.
Thank you Sir.
Respect, from India
I'm learning from Saudi Arabia. And I couldn't agree more with what you wrote! God bless him!
Hmm...I wouldnt go that far. Imho, he is a good teacher from what I've seen here. He clearly cares about teaching, and he engages his students the way a good teacher should. He starts from first principles and assumes next to nothing about his students. But I wouldn't call it artistry or a masterpiece of teaching haha.
Despite his humble comments, he actually is a Rembrandt.
@@MLFranklin so true
Yes... it's interesting how you can't really just rely on a book, and why it helps to watch a person actually doing it. And the style totally is important.
An amazing first lecture, glad to see the audio is fixed, thanks for taking care of this course. It's beautiful to perceive people from all over the world gathering here to gain knowledge, Professor Strang is a great teacher
For everyone begining this lectures that have no notions of linear algebra, I reccomend you to watch 3Blue1Brown series before because he put a lot of image on the word. Sorry for the mistakes, I am not an english speaker.
That series was amazing
Currently watching that series myself and would recommend it as a phenomenal starting point for Linear Algebra @3BLUE1BROWN
@Chris Metcalf i got my eyes on landing a job in data science for myself, just brushing up the mathematics behind machine learning but definitely not planning on doing deep theoretical tinkering and what not
what should i watch? the essence of linear algebra?
@@nerdpotato9368 yes
Hi professor and online collegueas. I'm a control engineering student, so Linear Algebra is the essential of my field of study. Despite I've taken a linear algebra course before and even sophisticated discussions in control systems, I never truly understood until now why it is better to think using columns instead of using rows. But now it's totally clear in my mind, so thank you very much, professor Gilbert. I'm anxious for the next classes.
its insane that this video is 15+ years old and still so valuable to someone beginning to learn linear algebra like myself
WTF? How old are you? 10? What 15 miserables years are to the Greatness of Mathematics!??? Math rules the Universe!
Same here!!
Because mathematics doesn't change
@@Dontpushyour_luck Until another Leibniz comes along
Have you finished it, was calculus prerequisite?
It's so important to develop a geometric view of linear algebra.
Kept 1st lecture intro to one minute. Bless this man.
Please spread this school on your wall and your friends because students need to see it.
So will you.
There are more than 4 000 tasks and theorems for primary and secondary school students.
Thank you for your contribution.
Respect! ........................................... .Të lutem shpërndaje këtë shkollë në murin tuaj dhe miqve tuaj, sepse nxënësit kanë nevojë ta shohin.
Kështu do të kontribosh edhe ti.
Janë më tepër se 4 000 detyra e teorema për nxënës të shkollave të nivelit fillor dhe të mesëm.
Faleminderit për kontributin tuaj.
Respekt!
ruclips.net/channel/UCELXh5_dCYX6umKP3qlOL9g
He is truly the Rembrandt of linear algebra. I’m deeply grateful to everyone involved in ensuring these masterpiece lectures were recorded.
That makes me remember the first semester linear algebra lecture. He certainly takes his time to explain, what the interpretation is and that is wonderful. We were not so lucky unfortunately.
Gracias Dr .Strang ,yo estudie algebra lineal con su libro ,pero verlo a Ud ,explicando en ingles , me llena de emoción , desearóa estar en su clase ,es un genio ,en persona es mas de lo que pueda decir su libro ,Mi admiración y respeto , Que calidad magistral para explicar algo tan ABstracto ,lo hace ver facil y sencillo,tanto que hasta mi hija de 12 años que esta en primaria lo entiende ,es un superhiperExplicador
Es un maestro a carta y cabal.
Preparing for IIT/IISC M.S interviews. IIT Madras, Electrical Engineering department had recommended this lecture
I am preparing for Gate(next year). How much have you done?
Me too preparing for Gate exam
Me preparing for iit jam
about to cry of how beautiful this is
humans will start learning machine learning here.
Yes, I'm here because of machine learning
@@bouthaina7846 hi
can you tell me what is the application of Linear Algebra in ML ?
I really confiused whit vector space and Scalar field and what we exactly model and do in linear algebra
@@rezaadventures actually I'm so new and just started studying machine learning but for what I've seen in neural networks, PCA and a lot more things everything is about matrices and linear algebra so I've decided to firstly understand linear algebra then everything else will be quite easy ...
@@bouthaina7846 Do u study computer science before or directly do machine learning ?
@@moonriver7632 yes I studied cs first
The cameraman here is now a Senior ML Engineer at Google, California.
@Bob Smith It's a sarcasm to the fact that how good these lectures actually are. 😅
@Bob Smith That kinda dumb is acceptable in the nerd academy so no r/wooosh for you.
@@aadarshmishra2504 very useful
r/woosh
😂
as a 1st year grad student a very long time ago, i took a course in linear algebra using Gil Strang's book. learning about the relationship between the four fundamental spaces of a matrix felt revelatory at the time, and i still have that book. he's such a wonderful expositor.
This makes me want to applaud. I watched his summary lecture that reiewed this course and I damn near clapped in my home. I should buy his book - I bought another one that's working fine, but didn't emphasize the row space column space null space left null space fundamental theorem of linear algebra picture that this course develops.
I love the quirky teaching style of Prof. Strang, especially how he feigns to encounter something surprising, whereas in fact it is well-rehearsed.
I can see why Dr. Strang is a professor at MIT. The best of the best.
❤0:54 the fundamental problem of linear algebra
- a system of linear equations needs to be solved
1:13
1:25
❤1:49 "picture a column at a time"
2:02
2:12
2:59
3:10
3:34
3:40 A is the matrix of coefficients
5:57
6:23
The line of solutions to this equation
8:34
14:13
23:44
26:00 big picture
29:30 multiplying a matrix by a vector. AX
Prof Strang really LOVES teaching, his soul is part of it-they say a genius make poor teachers- he is the one exception- Thank you for your efforts to bring people into your world
SO fantastic！！！THE Right way to open Linear Algebra!!! 我是来自中国的学生，当我认真学习线性代数的第一堂课后，我被深深的shocked到了！让我重新理解了维度！ N-D space is a combination of N-1-D sapce and non-N-1-D vector!
guys if you are here because of machine learning then trust me this course is the most most useful one to do before even starting machine learning i can ensue you it worth it 100% i myself have completed this series and it just gave me leg up in ML trust me after this course you will be able to understand ml concept that some of highly paid ML people can't! it will be such a leg up in you ml career i swear i wish i can erase it from my memory and do all it all over again
p.s please do it right tho understand every concept go through book and do exercise if needed give it good 3 months atleast
This is best Linear Algebra Course one can find on the internet
I had 3 semesters math in informatics study. This guy is way better than my prof years ago. He explains it way better
There are so many moments when I wanted to give this video an extra LIKE! He's such a good teacher!
Soy arquitecto, antes de ingresar a la facultad ingresé también a matemática pura, lamentablemente dejé las matematica por la arquitecturas, ahora devoro libros de matemáticas, espero algun dia retomar mi camino, mientras tanto me divierto con sus clases....y la pasión aumenta.
Saludos!
I always dreamed (and still continue) about studying at MIT, but I am not a genius and not a daughter of some deputy, so instead of university lectures I watch this course and imagine myself studying there))
hopefully you reach there :)
There's not that much difference on content on the subjects between good universities and the ones at the ivy league, just study for the love of it.
Luciano Rodriguez this is true. I attend an Ivy League university and paradoxically, the intro level math classes are awful, I study from MIT materials
I mean you also have to think about the school fees and see if it's worth it. I don't think it's as black and white as you may think, it's probably more grey.
That's passion. Great thought.
thank you Mr Strang for your lecture!!! i don't understand yet the fact that with 2 millions subscribers, only 4000 folow your lecture!! Your chain is one of the best i found regarding basical science, congratulations!!!
In the first lecture, from 14:10 to 15:26 the dude threw on the gem. If you notice this is the idea of vector spaces something which really you don't understand when you start linear algebra. Moreover, he pushed the argument at 22:00 with all the beauty to show that a column picture is a preferred way of looking when it goes into a higher dimension, the point on which he comes back in vector spaces. Finally, at 28:00 he concludes an important thesis for vector spaces.
For a person who is not really good at math, I hope this will really help me to develop a big picture of what linear algebra is. Thanks Prof. Strang.
This might help others trying to learn this material.
I found it easiest to watch a few lectures, but without being overly concern about learning exactly whats going on. This gives you a basis to work from.
Then get the text book and work though it slowly. Write down the examples in the book as you encounter them and get used to forming a mental picture for whats going on.
The column picture is key.
The row picture is probably what your school math teacher taught you. This just confused me a lot. I don't like dot products, but the "combinations of columns" is very intuitive once you can visualize why it works.
The reason I found this easier is that the concepts introduced in the videos are a bit loose, its just an overview. The real learning comes from the text book.
Fantastic explanation for column based geometry.
I had linear algebra over 40 years ago, but this was the first time I'd seen it presented this way. I've done fine in my engineering career, but this kind of thinking would have definitely made a few things easier.
I'm a student in Ariel University at Israel. I'm studying computer science and math, and I just want to say that you are a terrific teacher!
I will recommend your lectures to my friends for sure!
Thank you a lot.
Free Palestine
does this mean that in aany country most people do not study from college clases
Linear algebra had been mystery for me until I saw these types of lecture online. Thanks
I'm studying in McGill and this man is saving lives. Ofc, cramming before the finals :D God bless this man. Watched his videos on 1.25x speed
Nice to see a fellow McGillian! I graduated in 2016.
10 years ago I skipped Lin Algebra class and learned by watching this fantastic series of lectures. Moved to have learned that Prof Strang just retired. A big thank you to him for delivering such well thought through and well paced lectures.
I'm really happy that great lectures are available for free. Young people should appreciate it that they have internet and they can learn from materials from other universities especially from other countries from another part of the globe.
One of the best teachers! As a viewer of this course you feel the passion and love for math. He feels the math and can transfer his knowledge to other people. Well explained! Top!
This man is the best LA professor ever and these lectures are perfectly made. I really appreciate Prof. Strang and all the team involved.
Today was Gil’s very last lecture and retirement day. Happy Retirement Dr. Strang!!!
Superb clarity.world renowned professor of Mathematics.see how he acts on the stage one should inspire.I grace your heels.
Even though I've learned Linalg from my undergraduate course, it was ages ago. Thanks to Prof Strang, the explanation of the geometry meaning of the matrix is much clearer than what I've ever been given.
Wait, this was published 4 days before I decided I needed this? Thank you!
i guess they have re-uploaded the video again after fixing the audio channels. check their pinned comment before 1 month ! enjoy :)
You know a man's the GOAT if lectures from almost 2 decades ago with chalk and a blackboard are better than 90% of the content online. Thank You, Professor Strang and MIT for bringing such amazing content to the world...
When we get linear equations, Ax=b, where A is an n x n matrix, and x and b are column vectors with n components, we can see b as the linear combination of column vectors of A and components of x is equals to b. That is,
column 1 of A * 1st component of x
+ column 2 of A * 2nd component of x ...
+ column n of A * nth component of x.
This view is new for me. Thank you, Prof. Strang.
Why is Prof. Strang so successful at teaching? It's not just that his explanations are clear and reasonable. His personal style has a lot to do with it. He comes across as unpretentious and as someone who is doing this journey with you.
I can see in the class of this excellent professor and mathematician what the real problem in mathematical education is: our obsession to cover the topics always skips the necessity of the students to form the proper intuition of a topic. Intuition takes time, but above all takes proper activities to develop it. His talk is basically about the generation of spaces through linear combinations, but honestly could anyone sitting down there and listening reproduce those ideas without the help of proper representations, say, software, or at least good pictures? In mathematics, physics etc, intuition is the most important, but scholastic education has always tortured them with logic. That is totally unfair and a waste of talented students.
Why u say it is devoid of intuition when he is showing exact steps of logic? Sure, u may miss understanding the steps of logic, but nothing he is saying depends on intuition! Follow the formula correctly, get the right answer! Make a mistake in calculating, get the wrong answer!
@@davidjohnson497 🤦♂️
U can pause and think for yourself.
Dr Strang is a Legend, Thank u Sir and MIT for this awesome
course
Collect Mr Strang's lectures like a puzzle now (Because he's really good)
I don't think anyone could have explained it as good as this guy, props to him and everyone involved to make this happen!
24:44 thanks to prof. strang that he didn't get away by just taking an easy example and explained other cases where it didn't work.
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32:20 the way professor strang visualise the 9 dimensions is so impressive
Linear Algebra runs in his blood (Prof. Gilbert Strang). I now understand Linea Algebra thanks to his amazing lectures and his too much insight into this subject!!! He opens mind and unlocks concepts which are not naturally easy to grasp.
Thank you MIT OpenCourseWare..Prof. Strang is God, Not only MIT students the whole World deserves a great teacher like him.
A student from India
this course is good for under graduate student
The clearest explanation with clearest English. That accent is very clear and manly.
My lecturer in Linear Algebra was pretty good at doing mathematics but he was not so good at explaining it. I have really enjoyed these lectures and came back to the start just to encourage others to watch and enjoy.
Well boys, future starts here.
thats the greatest explanation of geometry of linear equations i have ever seen, thank you for everything sir, greetings from istanbul technical university
The only disappointment for me is the fact that Prof. Strang can't see my submission to his excellence and gratitude for his contribution, as I feel every time I see him.
At 20:50 This is why studying at MIT is worth the tuition. Great teacher!
Thanks for this; the impact of these videos on Linear Algebra education can't be overstated!
🎯 Key Takeaways for quick navigation:
00:55 🎓 *The first lecture of MIT's linear algebra course focuses on solving systems of linear equations.*
04:08 📊 *Linear equations are represented as Ax=b, where A is the coefficient matrix, x is the vector of unknowns, and b is the right-hand side vector.*
08:47 🖼️ *The column picture of linear equations involves finding linear combinations of column vectors of the coefficient matrix to produce the right-hand side vector.*
14:59 💡 *All possible linear combinations of column vectors fill the entire space of achievable right-hand side vectors.*
20:58 📐 *In three dimensions, the row picture of linear equations involves planes, where the intersection of these planes represents the solution.*
25:39 🧠 *Lecture on elimination methods for solving linear equations is upcoming, crucial for software and production applications.*
26:38 🔄 *Changing the right-hand side of linear equations can produce unique solutions, impacting both row and column perspectives.*
28:31 ❓ *Can the linear combinations of matrix columns fill three-dimensional space? Answering this question is crucial for solving equations for every right-hand side.*
31:40 ❌ *If matrix columns lie in the same plane, the matrix is singular, and not all right-hand sides have solutions.*
33:32 🌌 *Understanding linear combinations of vectors in higher dimensions is essential for grasping linear algebra concepts.*
35:45 🔄 *Matrix form of equations, A*x=b, highlights the importance of matrix-vector multiplication, viewing it as combinations of matrix columns.*
Made with HARPA AI
Even his voice sounds like a professor. Thanks for the upload!!🎉
So many questions answered in 40 minutes. Thank you so much, Professor Strang.
Comman man's Justice League:- Batman, Superman, Wonderwoman, Aquaman
My Justice League:- Gilbert Strang, Walter Lewin, Ben Polak, Patrick JMT, Ben Lambert
This is an amazing lecture for Linear Algebra. Thank you Prof. Strang!
I don't want to write down a big definition, you can see what it is."
how much we need teachers like this.
The Business Analytics admission director for McCombs school of business told me to watch these videos for a understanding of linear algebra.
I like the column perspective.
attend to the strang paradox; a vector field of unfinished sentences that form the basis vectors for a stunning range of interesting algebraic problems
That’s why people goes to MIT. What a class!
Can't remember last time i was so pleased learning maths, apart from a few 3b1b vids.
Thanks Sr.
Thank you Dr. Gilbert Strang. I am a senior lecturer at Azerbaijan State Agrarian University. I teach the subject Linear Algebrain in English . You explain very clearly.
I came here just for fun, but end up knowing something new. A new and easy method to multiply matrix. Thank you so much 🥰
I enjoyed this lecture. Professor Strang seems like a congenial person truly interested in imparting his knowledge. Some professors seem to look down on their students and have the attitude that if you don't get it, tough.
Really got the points!
First time in my life I have completed a lecture on math and also learned multiple new things!
All concepts got cleared.
Thank you Gilbert Strang for introducing me to LA.
Respect++;
Future employer: where did you study?
Me: MIT
Future employer: you’re hired!!
Amazing! I like linear algebra a lot, I already had this class in college, I keep reading about it and ... I didn't even notice the passing of 40 minutes of the first class you! No wonder MIT is a world reference!
1 o n 2[. 77|530
My term 2 (semester 2) is about to start. There we have maths 2 and to prepare myself for that I am here.My Senior suggested me this.
I am in foundation level (1st year) of IIT MADRAS (India) BS in Data Science and Applications.
Seems good one!
Yet to explore more!
By the way Thanks to Respected Prof Gilbert and MIT.
Hii! I'm the same case as you, preparing for maths 2
In my whole life never did this matrix multiplication make me sense like why are we doing multiplication and addition to numbers in a box in a specific manner, which is very non-intuitive, But the column picture idea that you gave makes me think it is matrix is an awesome tool to the equations
THIS must reach RUclips top videos instead of a trash going on there.
Linear Algebra has been my good old friend for several decades, but now I see a fresh look at my friend that looks much younger, all this thanks to the amazing profession Prof. Dr. Gilbert Strang. The essence of the timeless reverence Guru Brahma proved again. I shall be going through the entire series, even though, I wish I had this opportunity a decade and half ago. 🙏
I olny had math until 6th form (around 12th grade) and i was invited one day to see a matrix class.
And let me tell after the first 14 minutes of this video i really felt in love with maths
I'm 10 minutes in and I gotta tell you, in this 10 minutes you've done more than one semester of my course in linear algebra
I wish I could have found these gem of videos much earlier in my life
This lecture is not just for once, you probably come back to see and will find new things that you didn't get it before.
It's such a privilege to watch this honourable man delivering a lecture. Your lectures are helpful, especially, to the people living in a conflict zone like Kashmir, where the lockdown extends for months and this time it is almost a year with the continuous lockdown. Your 39 minutes lecture takes us more than 60 minutes to stream because of 10 months long high-speed internet restrictions enforced on us by the government's fascist approach. We have to make do with whatever we can with 2G networks. The board appears blurry because of slow networks.
Thank you, sir. Thank you, MIT. Thank you, America. ❤
I have always preferred solving linear equations with matrices, it is my go-to method. I like it because it is faster, saves me from having to write all the variables at each step, and because it is so neat and compact makes it easier to find errors.
5:00 It's always easier to rearrange the equations to the point-slope form which makes plotting so much easier. y = 2x, and y = x/2 + 3/2.
13:00 It would be more helpful to draw the resultant vector, (0,3) first so the target is plainly visible.
Muito obrigado professor pela grande explicação da combinação Linear👏👏🇦🇴🇦🇴
"It's the right place to start".. now, ..continuous observation of logarithmic 0-1-2-ness Polar-Cartesian i-reflection z axis containment in/of the x-y plane vector-value, convergent con-sequence, positioning. This is the "long hand" breakdown of pure-math Actuality, point-line-circle log-antilog conic-cyclonic coherence-cohesion Timing-Spacing.
İnanılmaz iyi anlatıyor,tane tane ve anlaşılır. Teşekkür ederiz.
I passed my linear algebra with a 100%but I literally didn’t know shit why those are happening. Thank you Dr Strang for letting us know what is linear algebra truly about.
never seen liner equations ever and I am 15 and this guy explains it so perfectly