Загрузка видео...

Не удалось загрузить видео

Возникла проблема при загрузке этого видео. Это может быть связано с временными проблемами сети или видео может быть недоступно.

На главную

Prof. Gilbert Strang from MIT giving a lecture on Linear Algebra - solving a system of two linear equations using a matrix. He really was a great teacher! I think he is now retired.

Martin

24,485 subscribers

41,808 просмотров • 6 месяцев назад •via X (Twitter)

Anya Rossi• Live Now

Private livecam show

Комментарии: 0

Нет доступных комментариев

Здесь появятся комментарии из оригинального поста

Похожие видео

A 91-year-old professor is why Nvidia is worth $4 trillion. His name is Gilbert Strang. He teaches linear algebra at MIT. Every AI model on Earth runs on his course. The course has been free on YouTube since 2005. The videos have earned him nothing. MIT 18.06 opens with "The Geometry of Linear Equations." No advanced math. Strang takes a system of two equations, draws it two ways, and shows the class that a matrix is a picture, not an abstraction. The row picture is two lines that cross. The column picture is two arrows that sum to a target. Every neural network on Earth operates on the column picture. Strang first taught linear algebra at MIT in 1962. He wrote the textbook in 1976. It is on every serious engineer's shelf. Every quant fund, every ML lab, every rendering engine at Pixar is running his math. His central insight is that most people are taught matrices as bookkeeping. That is the first thing to unlearn. A matrix is a linear transformation. A linear transformation is a way of moving space. Once you see the space move, the math stops being algebra and becomes geometry. The Kalman filter is a linear system. PCA is a linear system. Every gradient step in a neural net is a matrix-vector product. GPT is a stack of matrix-vector products, each one a scene from MIT 18.06 running on a Blackwell GPU. He retired in 2023 after 61 years at MIT. The course is still up. Watched tens of millions of times. The chip is $40,000. Strang never asked for a royalty.

A 91-year-old professor is why Nvidia is worth $4 trillion. His name is Gilbert Strang. He teaches linear algebra at MIT. Every AI model on Earth runs on his course. The course has been free on YouTube since 2005. The videos have earned him nothing. MIT 18.06 opens with "The Geometry of Linear Equations." No advanced math. Strang takes a system of two equations, draws it two ways, and shows the class that a matrix is a picture, not an abstraction. The row picture is two lines that cross. The column picture is two arrows that sum to a target. Every neural network on Earth operates on the column picture. Strang first taught linear algebra at MIT in 1962. He wrote the textbook in 1976. It is on every serious engineer's shelf. Every quant fund, every ML lab, every rendering engine at Pixar is running his math. His central insight is that most people are taught matrices as bookkeeping. That is the first thing to unlearn. A matrix is a linear transformation. A linear transformation is a way of moving space. Once you see the space move, the math stops being algebra and becomes geometry. The Kalman filter is a linear system. PCA is a linear system. Every gradient step in a neural net is a matrix-vector product. GPT is a stack of matrix-vector products, each one a scene from MIT 18.06 running on a Blackwell GPU. He retired in 2023 after 61 years at MIT. The course is still up. Watched tens of millions of times. The chip is $40,000. Strang never asked for a royalty.

Ochob

131,686 просмотров • 3 месяцев назад

Gilbert Strang taught linear algebra at MIT for fifty years. His last lecture is on YouTube. It has fewer views than his worst lecture. Nobody told students it was the last one. He just walked in, said "the final class in linear algebra at MIT," and started reviewing old exams. Google built a $2,000,000,000,000 company on one concept from this course. He is 88 years old. He still answers emails. This is MIT 18.06. Linear Algebra. The most watched mathematics course in history. Then the Markov matrix. Strang writes a transition matrix on the board. Three states. People moving between them every step. After enough steps - the system locks into a steady state that never changes. That steady state is an eigenvector. Google's PageRank works the same way. Websites are states. Clicks are transitions. The importance of every page on the internet is one eigenvector of one enormous matrix. Then least squares. Three data points. No line passes through all three. So you find the line that minimizes total error. That is how every AI model on earth is trained - including the ones running inside Goldman Sachs trading desks. Then the projection. The closest point on a plane to a vector outside it. Strang draws it in 30 seconds. That same operation is how Netflix decides what to recommend to 280,000,000 subscribers. Watch the moment he gives back the final exam answer and asks students to work backwards to the question - the room solves it in silence faster than any other lecture all semester. A software engineer told me 18.06 was the course that got her from $90,000 to $200,000 in two years. Same company. Different title. Bookmark this and watch later - after this lecture every dataset you touch will feel like a geometry problem waiting to be solved. MIT 18.06 Lecture 34 | Linear Algebra Final Review | Gilbert Strang

Gilbert Strang taught linear algebra at MIT for fifty years. His last lecture is on YouTube. It has fewer views than his worst lecture. Nobody told students it was the last one. He just walked in, said "the final class in linear algebra at MIT," and started reviewing old exams. Google built a $2,000,000,000,000 company on one concept from this course. He is 88 years old. He still answers emails. This is MIT 18.06. Linear Algebra. The most watched mathematics course in history. Then the Markov matrix. Strang writes a transition matrix on the board. Three states. People moving between them every step. After enough steps - the system locks into a steady state that never changes. That steady state is an eigenvector. Google's PageRank works the same way. Websites are states. Clicks are transitions. The importance of every page on the internet is one eigenvector of one enormous matrix. Then least squares. Three data points. No line passes through all three. So you find the line that minimizes total error. That is how every AI model on earth is trained - including the ones running inside Goldman Sachs trading desks. Then the projection. The closest point on a plane to a vector outside it. Strang draws it in 30 seconds. That same operation is how Netflix decides what to recommend to 280,000,000 subscribers. Watch the moment he gives back the final exam answer and asks students to work backwards to the question - the room solves it in silence faster than any other lecture all semester. A software engineer told me 18.06 was the course that got her from $90,000 to $200,000 in two years. Same company. Different title. Bookmark this and watch later - after this lecture every dataset you touch will feel like a geometry problem waiting to be solved. MIT 18.06 Lecture 34 | Linear Algebra Final Review | Gilbert Strang

Zyphor

56,603 просмотров • 1 месяц назад

The most important equation in statistics is the Normal Equations AᵀA x̂ = Aᵀb. It's the foundation of linear regression. Source: Professor Gilbert Strang, MIT.

The most important equation in statistics is the Normal Equations AᵀA x̂ = Aᵀb. It's the foundation of linear regression. Source: Professor Gilbert Strang, MIT.

tetsuo

74,943 просмотров • 11 месяцев назад

I got a viewer request to solve this system of linear equations

I got a viewer request to solve this system of linear equations

Howie Hua

17,249 просмотров • 10 месяцев назад

Rössler Attractor: A system of three non-linear ordinary differential equations.

Rössler Attractor: A system of three non-linear ordinary differential equations.

The Math Flow

39,417 просмотров • 6 месяцев назад

Gilbert Strang, MIT professor: "Anthropic pays $500,000 for one skill: linear algebra. a professor who gave 66 years to MIT taught all of it in his final lecture, for free." the article above hands you an AI that prints trading models on demand. strip the wrapper off any of them and one object is left. a matrix. Strang spent his whole career on that one thing, and this was the last time he ever wrote it on a chalkboard. look at what he puts up. A x = 0. the null space. it is every mix of your signals that cancels to nothing. an AI will hand you a thousand factors and half of them live right there, pure risk, zero return. a model is a covariance matrix, a set of eigenvectors, one projection. that is the entire machine. no magic, no black box. he was 88, and this was his last class ever. the recording sits free on YouTube while people pay for a worse version of what he gave away. the AI builds the matrix. Strang teaches you to read it. only one of those two skills holds its price.

Gilbert Strang, MIT professor: "Anthropic pays $500,000 for one skill: linear algebra. a professor who gave 66 years to MIT taught all of it in his final lecture, for free." the article above hands you an AI that prints trading models on demand. strip the wrapper off any of them and one object is left. a matrix. Strang spent his whole career on that one thing, and this was the last time he ever wrote it on a chalkboard. look at what he puts up. A x = 0. the null space. it is every mix of your signals that cancels to nothing. an AI will hand you a thousand factors and half of them live right there, pure risk, zero return. a model is a covariance matrix, a set of eigenvectors, one projection. that is the entire machine. no magic, no black box. he was 88, and this was his last class ever. the recording sits free on YouTube while people pay for a worse version of what he gave away. the AI builds the matrix. Strang teaches you to read it. only one of those two skills holds its price.

Rossst.03

70,698 просмотров • 1 месяц назад

IN 1999 MIT FILMED A MATH LECTURE THAT QUIETLY BECAME THE FOUNDATION OF EVERY AI MODEL YOU'VE EVER USED AND ALMOST NO ONE WAS TAUGHT TO SEE IT THAT WAY 39 minutes from Gilbert Strang, who taught this at MIT for over 60 years -- the linear algebra course an entire generation of engineers and data scientists grew up on. -> The shift it creates: you stop seeing matrices as boring grids of numbers and start seeing them as the language of space, data, and motion itself. School drilled you to crunch matrices by hand and never told you why. Strang shows you what they actually mean. Every neural net, every embedding, every model you prompt is linear algebra running underneath. The math you skipped is the engine of the thing you use all day. Memorizing the steps was never the skill -> seeing what the numbers do is. This is where it finally clicks. Most people fear linear algebra and move on. The ones who watched this see straight into how AI actually works. Bookmark & Watch it today, this one's a legend ↓

IN 1999 MIT FILMED A MATH LECTURE THAT QUIETLY BECAME THE FOUNDATION OF EVERY AI MODEL YOU'VE EVER USED AND ALMOST NO ONE WAS TAUGHT TO SEE IT THAT WAY 39 minutes from Gilbert Strang, who taught this at MIT for over 60 years -- the linear algebra course an entire generation of engineers and data scientists grew up on. -> The shift it creates: you stop seeing matrices as boring grids of numbers and start seeing them as the language of space, data, and motion itself. School drilled you to crunch matrices by hand and never told you why. Strang shows you what they actually mean. Every neural net, every embedding, every model you prompt is linear algebra running underneath. The math you skipped is the engine of the thing you use all day. Memorizing the steps was never the skill -> seeing what the numbers do is. This is where it finally clicks. Most people fear linear algebra and move on. The ones who watched this see straight into how AI actually works. Bookmark & Watch it today, this one's a legend ↓

slash1s

435,509 просмотров • 4 месяцев назад

I took Gilbert Strang’s course at MIT, and it profoundly shaped how I think. One fun memory: an acappella group stormed into class on Valentine’s Day to serenade a student, Prof Strang was thoroughly amused! MIT CSAIL

I took Gilbert Strang’s course at MIT, and it profoundly shaped how I think. One fun memory: an acappella group stormed into class on Valentine’s Day to serenade a student, Prof Strang was thoroughly amused! MIT CSAIL

Pinar Yanardag

50,390 просмотров • 4 месяцев назад

How can we find all integer solutions to 3x+2y=100? Here's a quick introduction to solving linear Diophantine equations.

How can we find all integer solutions to 3x+2y=100? Here's a quick introduction to solving linear Diophantine equations.

Howie Hua

14,181 просмотров • 7 месяцев назад

$MIT FILMED THE LECTURE WHERE THEIR MOST LEGENDARY LINEAR ALGEBRA PROFESSOR EXPLAINS WHY EVERY GPS SIGNAL EVERY MEDICAL SCAN AND EVERY AI MODEL ON EARTH IS SECRETLY SOLVING A PROBLEM THAT HAS NO SOLUTION This is Gilbert Strang, MIT, 18.06 Linear Algebra, lecture 15. The professor whose textbooks sit in over 3,000 universities across 135 countries and whose course has been watched by millions of engineers and mathematicians worldwide. He opens with one claim - when equations have no solution, you do not give up. You solve the closest problem that can be solved. He starts with a vector b and a line through a. The projection of b onto that line is the point closest to b that actually lives on the line. The key is a right angle. The error - the gap between b and its projection - must be perpendicular to a. That one geometric fact produces the entire formula. The projection is a times a transpose b divided by a transpose a. One fraction. The numerator is a matrix. The denominator is a number. Then the projection matrix. Every projection is carried out by a matrix P that multiplies b and lands on the line. That matrix has two properties that define all projections everywhere. First, P transpose equals P - the matrix is symmetric. Second, P squared equals P - project twice and you stay where you are. The first projection moves you onto the line. The second leaves you there. Then higher dimensions. Instead of projecting onto a line, project onto a plane. Instead of one vector a, you have a matrix A with two columns spanning the plane. The error vector must now be perpendicular to both columns - perpendicular to the entire plane. That condition produces one matrix equation. A transpose times the error equals zero. The error lives in the null space of A transpose, which is exactly perpendicular to the column space of A. The four fundamental subspaces appear without being called. Then the formula for n dimensions. The projection matrix is A times A transpose A inverse times A transpose. Strang warns the room not to simplify it by canceling A inverse against A - A is not square, it has no inverse, and the formula cannot be pulled apart. The only case where it simplifies to the identity is when A spans the whole space and the projection is b itself. Watch the moment he applies the formula to fitting a line through three points that no line can pass through. Three equations, two unknowns, no solution. He writes the matrix, writes the right-hand side, and shows that multiplying both sides by A transpose produces an equation that always has a solution. That equation is the foundation of least squares, GPS triangulation, and every regression model trained in 2026. A data scientist I know rewatched this lecture before building a recommendation system from scratch. Said it was the first time the normal equations felt like geometry rather than a formula someone handed down to memorize. Free on YouTube, MIT OpenCourseWare, filmed over 20 years ago. bookmark this and watch later - after this lecture every unsolvable equation you meet will feel like a projection waiting to be found$

MIT FILMED THE LECTURE WHERE THEIR MOST LEGENDARY LINEAR ALGEBRA PROFESSOR EXPLAINS WHY EVERY GPS SIGNAL EVERY MEDICAL SCAN AND EVERY AI MODEL ON EARTH IS SECRETLY SOLVING A PROBLEM THAT HAS NO SOLUTION This is Gilbert Strang, MIT, 18.06 Linear Algebra, lecture 15. The professor whose textbooks sit in over 3,000 universities across 135 countries and whose course has been watched by millions of engineers and mathematicians worldwide. He opens with one claim - when equations have no solution, you do not give up. You solve the closest problem that can be solved. He starts with a vector b and a line through a. The projection of b onto that line is the point closest to b that actually lives on the line. The key is a right angle. The error - the gap between b and its projection - must be perpendicular to a. That one geometric fact produces the entire formula. The projection is a times a transpose b divided by a transpose a. One fraction. The numerator is a matrix. The denominator is a number. Then the projection matrix. Every projection is carried out by a matrix P that multiplies b and lands on the line. That matrix has two properties that define all projections everywhere. First, P transpose equals P - the matrix is symmetric. Second, P squared equals P - project twice and you stay where you are. The first projection moves you onto the line. The second leaves you there. Then higher dimensions. Instead of projecting onto a line, project onto a plane. Instead of one vector a, you have a matrix A with two columns spanning the plane. The error vector must now be perpendicular to both columns - perpendicular to the entire plane. That condition produces one matrix equation. A transpose times the error equals zero. The error lives in the null space of A transpose, which is exactly perpendicular to the column space of A. The four fundamental subspaces appear without being called. Then the formula for n dimensions. The projection matrix is A times A transpose A inverse times A transpose. Strang warns the room not to simplify it by canceling A inverse against A - A is not square, it has no inverse, and the formula cannot be pulled apart. The only case where it simplifies to the identity is when A spans the whole space and the projection is b itself. Watch the moment he applies the formula to fitting a line through three points that no line can pass through. Three equations, two unknowns, no solution. He writes the matrix, writes the right-hand side, and shows that multiplying both sides by A transpose produces an equation that always has a solution. That equation is the foundation of least squares, GPS triangulation, and every regression model trained in 2026. A data scientist I know rewatched this lecture before building a recommendation system from scratch. Said it was the first time the normal equations felt like geometry rather than a formula someone handed down to memorize. Free on YouTube, MIT OpenCourseWare, filmed over 20 years ago. bookmark this and watch later - after this lecture every unsolvable equation you meet will feel like a projection waiting to be found

Lupen

24,677 просмотров • 2 месяцев назад

If you haven't introduced solving linear equations with bar models, I highly recommend it. Here's why:

If you haven't introduced solving linear equations with bar models, I highly recommend it. Here's why:

Howie Hua

24,475 просмотров • 1 год назад

New episode! Michael Nielsen joins tylercowen to discuss the beauty of the universe, quantum computing, Simone Weil, finding good collaborators, and...the status of linear algebra? COWEN: Is the status of linear algebra rising? NIELSEN: [laughs] That’s a great question. It probably has, yes. COWEN: It’s prominent in quantum, right? It’s prominent in AI. NIELSEN: Google is built on matrix multiplication. It’s prominent for a lot of reasons. COWEN: What should we infer from that about the whole nature of the world?

New episode! Michael Nielsen joins tylercowen to discuss the beauty of the universe, quantum computing, Simone Weil, finding good collaborators, and...the status of linear algebra? COWEN: Is the status of linear algebra rising? NIELSEN: [laughs] That’s a great question. It probably has, yes. COWEN: It’s prominent in quantum, right? It’s prominent in AI. NIELSEN: Google is built on matrix multiplication. It’s prominent for a lot of reasons. COWEN: What should we infer from that about the whole nature of the world?

Conversations with Tyler

94,765 просмотров • 2 лет назад

This is a great lecture at MIT by David Shirokoff on Markov Chains. He covers the fundamentals of Markov Chains using a simple particle movement example. He starts by explaining how a particle moves between two positions, A & B, with different probabilities. From there, the talk converts the problem into matrix form using a Markov matrix. The main topics covered are: - Transition probabilities - Markov matrices - Probability vectors - Matrix multiplication in Markov Chains - Finding probabilities after n steps - Eigenvalues and eigenvectors - Matrix diagonalization - Long-term steady state distribution

This is a great lecture at MIT by David Shirokoff on Markov Chains. He covers the fundamentals of Markov Chains using a simple particle movement example. He starts by explaining how a particle moves between two positions, A & B, with different probabilities. From there, the talk converts the problem into matrix form using a Markov matrix. The main topics covered are: - Transition probabilities - Markov matrices - Probability vectors - Matrix multiplication in Markov Chains - Finding probabilities after n steps - Eigenvalues and eigenvectors - Matrix diagonalization - Long-term steady state distribution

𝗿𝗮𝗺𝗮𝗸𝗿𝘂𝘀𝗵𝗻𝗮— 𝗲/𝗮𝗰𝗰

142,204 просмотров • 5 месяцев назад

When I got into a huge Student Debt, but some random dude on the Internet is using Linear Search instead of a Hash Table! Absolutely infuriating!

When I got into a huge Student Debt, but some random dude on the Internet is using Linear Search instead of a Hash Table! Absolutely infuriating!

Тsфdiиg

52,621 просмотров • 2 лет назад

Graph theory & Linear Algebra.

Graph theory & Linear Algebra.

ₕₐₘₚₜₒₙ

153,911 просмотров • 2 лет назад

Ben Affleck says AI is simply matrix multiplication, linear algebra and floating point calculations, and however convincingly it sounds like a person, it has nothing to do with thought, humanity or feeling “Nor do I believe, and I think it’s important to draw the distinction between what AI does, which is simply predict the next token or the next word in a sentence, then add that word on, run it back to the machine, do a lot of computation and pick the next word." "That is a very different thing than sentience or thought. And I think we need to be really clear about that because it can be convincingly, in an illusory way, sound like thought or like a person." "But let’s be real clear. This is matrix multiplication. This is linear algebra. These are floating point calculations. It has nothing to do with thought, humanity, or feeling.”

Ben Affleck says AI is simply matrix multiplication, linear algebra and floating point calculations, and however convincingly it sounds like a person, it has nothing to do with thought, humanity or feeling “Nor do I believe, and I think it’s important to draw the distinction between what AI does, which is simply predict the next token or the next word in a sentence, then add that word on, run it back to the machine, do a lot of computation and pick the next word." "That is a very different thing than sentience or thought. And I think we need to be really clear about that because it can be convincingly, in an illusory way, sound like thought or like a person." "But let’s be real clear. This is matrix multiplication. This is linear algebra. These are floating point calculations. It has nothing to do with thought, humanity, or feeling.”

Fireside Alpha

2,387,267 просмотров • 13 дней назад

Set Yourself on Fire is now available on Steam A linear visual novel. A quiet town awaits death. Stagnation is the default state of being. Two aimless young women fall in love.

Set Yourself on Fire is now available on Steam A linear visual novel. A quiet town awaits death. Stagnation is the default state of being. Two aimless young women fall in love.

Denhop

260,842 просмотров • 6 месяцев назад

Gilbert Strang, a quiet MIT professor, picked up a piece of chalk and explained the one skill standing between you and every account you have ever blown. MIT put the entire course online. it has been free for over twenty years. almost nobody finishes it. His point: the market never pays in certainties. it pays in probabilities, and a human gut can barely hold one straight. the math that holds ten thousand at once, weighs them, and collapses them into a single call is linear algebra. it is the branch Citadel and OpenAI both pay $400K to hire for. he is not a trading guru. his 18.06 lectures are the most watched math class on the planet. Skip to where he turns a wall of numbers into one vector. a single object carrying a thousand odds at once, in notation a beginner can follow. No slides. no jargon. one piece of chalk. a quant I know rewatches lecture one every year before he sizes a single position. You do not have a strategy problem. you have a math problem. the fix has been free for two decades, and you are still guessing.

Gilbert Strang, a quiet MIT professor, picked up a piece of chalk and explained the one skill standing between you and every account you have ever blown. MIT put the entire course online. it has been free for over twenty years. almost nobody finishes it. His point: the market never pays in certainties. it pays in probabilities, and a human gut can barely hold one straight. the math that holds ten thousand at once, weighs them, and collapses them into a single call is linear algebra. it is the branch Citadel and OpenAI both pay $400K to hire for. he is not a trading guru. his 18.06 lectures are the most watched math class on the planet. Skip to where he turns a wall of numbers into one vector. a single object carrying a thousand odds at once, in notation a beginner can follow. No slides. no jargon. one piece of chalk. a quant I know rewatches lecture one every year before he sizes a single position. You do not have a strategy problem. you have a math problem. the fix has been free for two decades, and you are still guessing.

Loran

47,557 просмотров • 3 месяцев назад

the first free interactive linear algebra textbook: - vectors and matrices - dot product and vector product - determinants - matrix ranks - eigenvalues and eigenvectors

the first free interactive linear algebra textbook: - vectors and matrices - dot product and vector product - determinants - matrix ranks - eigenvalues and eigenvectors

ℏεsam

63,641 просмотров • 1 год назад