Geometry of Linear Algebra
HTML-код
- Опубликовано: 12 сен 2024
- MIT 18.06SC Linear Algebra, Fall 2011
View the complete course: ocw.mit.edu/18...
Instructor: Linan Chen
A teaching assistant works through a problem on the geometry of linear algebra.
Watch this in Chinese: • 线性代数的几何表示
License: Creative Commons BY-NC-SA
More information at ocw.mit.edu/terms
More courses at ocw.mit.edu
I'm not going to say this is the only person I can learn linear algebra from. But after looking at 100's of videos from dozens of creators/providers, I get the topic faster from Linan Chen than anyone else I have come across. While the content (the curriculum) seems very similar to others, the slight but meaningful differences in the way it is presented make a lot of difference. The cadence, the choice of words, its hard to put my finger on the exact reason but clearly Linan has a gift for teaching.
I have been looking for over a week for an explanation of why polynomial linear regression uses A -1 * A and this video explains it unbelievably simply!! Amazing. One of the biggest "lightbulb moments" of my life. Thank you so much.
Can you explain what you meant here?
It's incredibly simple too understand.
These two linear equations are simple. This is like high school level. You would probably whine if she brought up something more complicated.
@@Sameerahmed373probably trying to understand how the vector of coefficients in poly regression are derived but without enough math literacy
@@patricks8364 you know actual high school kids watch this right? you like bullying kids?
Wow. Could she do this for every video? Amazing delivery. Kudos!
Linan has done such a good job on the explanation! Thanks, MIT OCW
Since the column picture visualizes the coefficients vectors, the axis labels for the column picture should not be x and y.
x and y - although variables - were impersonated as the 'dummy coefficients' for those vectors / linear combination.
Excellent point. I also felt the same. Naming the axis as p,q or a,b would have helped. Overloading x and y creates confusion.
These are the straightest hand written lines I've ever seen.
What about Walter lewin's lines
How's it hangin, Wang?
In China, Mainland teachers are always drawing lines like this. Also, they usually draw standard parabola lines as they can. When studends in China draw sketches, teachers will stress the importance of standard sketches drawing all the time. She was studying in Mainland China. Maybe, that' s why "These are the straightest hand written lines I've ever seen."
This is from the year I was born in. Now I’m self studying linear algebra. Currently at differential equations. I hope I make it into MIT for transfer. Hard as it may be.
Don't get me wrong, I think this recitation is expertly done, no question about that. However, I'm a bit disappointed that some of the more important insights from this row/column picture comparison wasn't made clearer to viewers. For example…
In the ROW picture, you're looking at variables X and Y as two dimensions of the plane. The lines (as dictated by the linear equations) depict two constraints that the solution (a combination of X and Y, i.e. a point on the plane) must simultaneously satisfy. You obviously find the solution by reading off the X, Y coordinates of the intersection point. More generally, there can be many, many constraints on a lot of variables, but each ROW only describes ONE constraint on ALL variables.
Whereas in the column picture, you're NOT looking at the X-Y plane anymore (as someone already pointed out). The number of dimensions of the space you’re looking at reflects the number of constraints imposed by the linear system you’re dealing with. Roughly speaking, the more equations (or more rows) you have, the more constraints there are, the higher dimensional the space is. A column (shown as a vector in the space) describes a transformation in that space to be scaled by a variable. Each variable has one transformation (one vector) associated with it. Then the system is simply a linear combination of those transformations, constrained by the condition that the end result must equal to the column vector on the right side of the equal sign - which itself is a transformation. You can think of a COLUMN as ALL the constraints on ONE variable. So, to solve the equations, you need to find combinations of variables that will collectively scale/combine all the transformations just the right way, so that the total effect is the same as the right-hand-side transformation.
But to be fair, a lot of this should have been introduced in the lectures, not as part of a recitation.
Sure. All of the ideas were given in the lecture. The recitation was kinda useless for me. Probably because I watched both of them on the same day. Lol. It's purpose might be for those people who go by actual University pace of like 2 lectures per week. I really miss University though 🥺
Thanks so much for your comment!
The number of dimensions depends on the number columns the A matrix has. For a square matrix A, the number of constraints equal the number of dimensions but for A bon square matrix A, the number of constraints is different from the number of dimensions
Excellent teaching! More videos from her please.
Looked her up to see what kind of Prof she has become, doesn't disappoint. Very highly rated professor.
Really? How did you find that?
@@investingshorts6021 Lol just look up her name at RateMyProfessors
@@algotrader9054 She is an associate professor at McGill University now.
Hi, I think in the column picture, it is advisable not to use the coordinates of the graph as x and y... this might confuse a student.
Besides that, every thing is just great!
Thank you!
True that
I love the expression of v1x+v2y instead of xv1+yv2. Because it seems easier to understand for beginner. (although scalar *vector is more common.) But last part regarding inverse matrix seems too difficult topic in this stage.
No wonder why MIT is recognized as one of the best schiool in the US. The students are so fortunate to have this quality of lecturers. I have study linear algebra with different teacher, and they were enable to make such a great review. THANK YOU MIT
She isn't even a lecturer. She is a Teaching Assistant meaning she herself is a student in a Master's or PhD course.
man!! the writing is so beautiful... when i tried to write on board in school it sucks...
explanation is way easy to go through...
She speaks in a mind-easing tempo, like a flying assistant does.
This teacher helps me get linear.
Just a suggestion: You have used x,y to stand for coefficients, then using xOy as vector coordinates could be confusing.
I agree that the x and y axes for the column picture are confusing. But, thinking for the other axes and their unit vector is very interesting for me. I feel I am in totally different space!
Linan makes me love Linear Algebra!
Best and clearest video covering vector and matrix for linear algebra
Gran explicación, muchas gracias.
OMG这个TA小姐姐也太有气质了吧
Yes smart and pretty. So rare !
这线性代数讲的真好看
The second coordinate plane should not be marked as xoy plane. The meaning of x, y was defined in the equations.
Wow. This is exactly what I needed. Thank you
Very Calming lecturer :)
thank u that what i was looking for !!!
That is a nice example. However, I have a doubt about the concept. We are using a row picture or a normal linear equation solving method to derive an answer and we are using that solution to depict the column picture. If that is the case what is the role of a column picture.
Thanks in advance for taking the time to see and reply to this one.
It's to visualize the methods
8:10 Columnpicture
Your Linear Geometry class is explanatory. Could you make new videos about other equations?
Best Regards!
Luís Lopes
Super teaching method......thank you so much for all......
She’s an amazing lecturer
"Why don't you pause the video now and try to work them out on your own." :) :) :)
I literally solved this for z instead of 2. It took me 5 sheets of paper and 80 minutes. I obtained 8 COMPLEX solutions. I don't know if I'm dumb or smart anymore.
Good job
Great presentation
Thank you so much.
Great presentation
Thank you
I literally thought that the "2" was a "Z" as another unknown variable.
Got me confused at the first 20 seconds :)
haha
LoL same here 😆😆😆
Thank you!! This was super helpful!!
At 15:00 how could a=0 if ax=b => x=b/a. Then, b is also 0
Very nice intro. Thanks
5:50 Row picture
clear and simple.
Excellent Camera work
Great video by great tutor
Why is Y not a i-grec?
ohh damn, You are good! Awesome explanation.
At 12:29 do you mean that's the column picture?
+1
Sorry，do anyone know if the
5th edition textbook by Professor Gilbert can match this course video ?it’s really important to me…😢
Each unit has been further divided into a sequence of sessions that cover an amount you might expect to complete in one sitting. Each session has a video lecture on the topic, accompanied by a lecture summary. For further study, there are suggested readings in Professor Strang’s textbook (both the 4th and 5th editions).
View the complete course: ocw.mit.edu/18-06SCF11
Best wishes on your studies!
@@mitocw ！！！i didn’t expect the official account to answer my question……(so lucky)thanks for warmhearted reply…….i ll do my best to learn it well😭
How should we find the x and y at the end
Handwriting goals
great class!
太好看啦！
Thank You!
This is linear asmr.
I can never reproduce these elegant hand writings.... lol...
莉楠，棒棒哒🎉
thanks ...🙏🙏🙏
`An amazingly bright young lass - and when I type into Google or RUclips " Review Row Picture" I`m directed to this video. Little wonder maths can be so trying.
Excelent !
omgggg, love it!
Please new video
Linan is really cute and knowledgeable
lodu chand
she is more than cute.
Linan Algebra *ba dum tss*
@@zombiesalad2722 Ghatlodiya lol
I'm finding materials to teach when I saw this. She's cute! Coming back here soon! 🙊
I have an great enthusiasm and intrest attend few programs in mit which are not free but I am not financially well . Can anyone help me out in suggesting the possible ways
MIT is one of only seven colleges in the U.S. that is need blind and full need for all of our undergraduate students, domestic and international. For most students with family incomes under $140,000 a year (and typical assets), we ensure that scholarship funding will allow them to attend MIT tuition-free. Tuition-free means your MIT Scholarship covers at least the cost of MIT’s tuition. See sfs.mit.edu/undergraduate-students/the-cost-of-attendance/making-mit-affordable/ for more info. Best wishes on your educational journey!
Superb
Wonderful. :)
6:27
14:00
3:49 row picture
4:52 2points on the plane
@MIT OpenCourseWare, in the description, it would be more appropriate to say the name of the teaching assistant than simply "A teaching assistant..."
In Viet Nam we learn this equation when we 15 year old.
89, 2525
Excellent but a little shy.
Could we get the result of the column picture without having to look at the row picture first ?
Yea, you can. They are just two different ways of solving a linear equation.
Yes, just draw the resulting vector b. Then draw the parallel line to v2 to pass through the tip of b and scale the v1 until it touches such new line. The resulting drawing gives a head-tail construction of a linear combination of v1 and v2 that gives you vector b.
super
Subtitles no need only disturbing
Anyone from biology related field.PLease reply
interesting accent
Gorgeous....
I mean the maths ...that math she is doing is gorgeous
国人🎉
how i can find her full playlist ???
@MITOPenCourseWare
Here's the full playlist to the course: ruclips.net/p/PL221E2BBF13BECF6C.
Visit MIT OpenCourseWare for more info and materials at: ocw.mit.edu/18-06SCF11.
Best wishes on your studies!