My god this is probably the best lecture I have ever witnessed. Her voice is so calm and clear and she writes so clean and perfect. There is no way one could not understand.

When I took a course on linear algebra at this time in 1976, we never looked at any geometric representations. It's no wonder I was so confused and frustrated!. This revelation comes 38 years too late, but better late than never. While I watched this video, I could feel my brain light up dendrites and neurons.

@anjanghosal4187

6 жыл бұрын

Way I look at it .. better late than never! :) I am taking this 33 years after completing engineering .. thanks to Machine Learning and AI!

@pauljohny200

5 жыл бұрын

This is a new better of way of education. .You have doubts you can even put comments peope from net will help . evne use facebook to ask and clear doubts. New world of internet ..All you need is intrest ,wish and desire and ofcourse a bit of brain

@davidlocke4977

4 жыл бұрын

I'm in the same boat. The geometric view makes linear algebra so much simpler.

@yetanotherchannelyac1434

3 жыл бұрын

Visceral indeed!

@chrismill9896

3 жыл бұрын

In 1968 I took a Linear Algebra course at Brandeis and didn't understand a word of it. It was all [ defn, theorem, proof} repeated endlessly. I didn't understand the questions, or my answers, even when they were marked correct, Absolutely a waste of time. Meaningless !

She explains everything in one's heart. You will learn in logical harmony, nothing remains open and this along with tenderness and beauty. Thank you very much.

Brilliant and yet simple explanation. Thank you very much! It looks like the row picture represents more the algebraic aspect and the column picture more the geometric aspect in a system of linear equations.

Such a beautiful explanation, that comparison with simple equation on real numbers really made this whole idea very intuitive.

Wow this is great, I'm so happy I found this channel!

Professor Linan Chen thank you for a beautiful explanation on the Geometry of Linear Algebra.

You are totally fantastic Linan ! thanks for a very clear presentation. I wish you were my math teacher.

This is the most creative presentation on linear algebra that I have ever seen.

Great Job coming up with a super clear example of the concepts with very little room for confusion.

OMG! I love you! Thank you so much!

Thank you so much for your explanation!

Thank you for a very clear lecture. It wasn't rushed and nothing extraneous. Plus you have a pleasing speaking voice. I used to teach calculus and I had a tendency to rush what I was covering. I learned from your stye well as content. Thank you again. I hope to find more of your lectures.

Great introduction to the subject. Very clear linear equation to vector addition connection. Well done.

This is the one of the best geometric explanation of matrices and linear equations 👏👏👏👍👍👍

You just solved my conundrum. Thanks. You are sooo helpful.

Wow, her calm voice and simple language is amazing and it makes learning a pleasure.

Dear MIT, You are the best. Your videos are easy to watch. We can fast forward, rewind, mix the videos and the videos are still making sense. Thank you for all these Masterpieces!

I love you teacher. From a student in Cambodia.

Thank you professor. This is so clear.

这口音听着真舒服! Nice video!!

That was an excellent explanation. Your explanation was perfectly paced. Thank you.

To simplify the calculations setting the x=1 as illustrated in slide of timing 4:36/16.35, I recommend to set both x and y on coordinate axes to initiate the geometry solution process. 2x + y = 3 (1) x - 2y= -1 (2) For equation 1, Set x=0, we get point a1 of (0, 3) Set y=0, we get point b1 of (1.5,0) Connect points a1 and b1, we get the first straight line. For equation 2, Set x=0, we get point a2 of (0,0.5) Set y=0, we get point b2 of (-1,0) Connect points a2 and b2, we get the second straight line. With Intersection of the two(2) lines, we have the geometry solution point s of coordinate (1,1), which sits on both straight lines. I'd done the drawing on a Word page, however, I don't know how to up-load the image.

thanks very much. it's very easy to understand the key point of linear algebra.

why did this make so much more sense than the main lecture of the course.....the ocw videos are like hey if your not a genius hang on.

Finally seeing myself in the mirror of concepts. THANKS A LOT.

Linan Chen you are very good ! Thanks a lot !

Short and direct! Tks Linan Chen! =)

i & j are bases vectors and x & y the lengths of vectors which actually scale i & j.there4, When doing vector approach it is not professional to use x and y axes. X and y are the lengths of the vectors not the axes system. Use i and j for axes.

Thanks for the wonderful explanation!

The best lecture I had on linear algebra. Thank u so much

As stated in Avenue Q when the subject of going back to college was being discussed, this T.A. sure does spark my interest.

More than nice. Excelent presentation, Thanks.

고맙습니다

Beautifully explained

The row picture and column picture by intersection with x and y axis forming a triangle and the area can be found out by formula.

Excellent presentation!

Good explanation ....I know the concept discussed here. The best thing in the video is the simple and lucid way of explanation.... Generally Math teachers always try to prove their dominance over the subject in front of students..

Immensely well taught!

Well done. Excellent and insightful.

What a gorgeous handwriting :D

@dogwithwigwamz.7320

3 жыл бұрын

Handwriting does help in mathematics - as you appreciate. Far better to be able to keep a record of progress made when you may read what has been written - and not struggle in fathoming the almost incomprehensible mess that accumulates during the course of videos produced by people such as The Khan Academy.

She's a great teacher!

Column vectors forming a parallelogram by diagonalisation clearly indicating a piezo electric effect on any crystal by diagonalisation.

Thank you very much for the lecture!!

i like this. it is good to see math on the youtube

both ears get educated. double bonanza. thank you MIT

Very good and interesting lesson ! Thank you !!! 😊

when I was taking high school algebra in the 90s, we did not have these terminologies such as row&column pictures. We have done only solving system of equations (elimination or substitution), finding the coordinates, plotting the equations in the graphing paper, looking for the coordinate at which the equations intersect in our graph as proof, and then move on to another problem. The concept of vector was not taught to us we only have coordinates.

I just watched this and also Strang and I see how it works using the vector form but I don't get how the entries of vector 1 can be plotted in the x , y plane as "x" and "y" coordinates if the entries of v1 represent exclusively the coefficients of the x variable in the two equations of the original system ? Is it arbitrary what 2D orthogonal axes are used?

this is a so cool lecture

great info. thank you.

fabuloso, gracias

muy bien explicado!

Thanks alot I appreciate

oh, thank you, words in the blackboard are very beautiful and the lecture is very simple and clear, thank you, Professor😊😊😊

非常棒！

Bravo, excellent explaination.

What a wonderful class. It makes me want to do maths problems.

Thank You!

Thank you

thank you so much you were very clear and you gave such a wonderFul explanation I wish you were my math teacher. Please keep up the good work Thanks.

Awesome teaching!

while looking in the row picture we take (2{of first equation},1{of second equation}) as x coefficients and (1{of second equation},-2{of second equation}) as y coefficients but when we try to look at column picture she just interchanged the axis while drawing the vectors ; she took (2{of first equation} as x & 1{of second equation} as y) where 1{of second equation} represents x axis in the row picture.

@redberries8039

6 жыл бұрын

...yes I have the same confusion

Mam, you are a very good teacher.

Happy new year😀🎉🎉

Amazing! !

thank you that was very helpful

Now I really find it so easy 😃

I am reading CLRS for three days,but couldn't understand anything but this video cleared the concept

Column picture is an amazing understanding, I have never seen it in Russia

Thank you lady

Thanks Prof Linan. There's one point in the video you should have said "column picture" but you said "row picture" instead. It doesn't really matter but I'm just pointing it out. I hope you make more videos. =)

muito interessante esses vidius aulas

She teach very well, and she s so cure too

Very good thank you

I do not understand the relationship between x and y in the equations and the X- and Y-axis in the column picture. Is there one?

@redberries8039

6 жыл бұрын

...same for me

Thankyou teacher

Thanks very well explained

between 3:24 and 3:3:36 , it is said 'let s find out what is row picture', 'first let s look at row picture'. But then at 3:38 it is said 'please review what a row picture is.' That is confusing. The rhetoric implies that a demonstration is upcoming. Yet, at 3:38, the main idea is that it is asked that self-directed review of the concept that is not yet seen be reviewed; while announced beforehand that a presentation of it is upcoming.

Esta clase es como las que me daba mi maestro en la preparatoria, en México.

So what is the exact use of column picture? Row picture and solving system of equations is giving me solution. But for Column picture she is using the solution arrived @row picture. So why do we need column picture. Is it just for verifying the answer

Verry good lecture Thanks

Terrific.

Mit always the best

i like this video about the geometry of Linear Algebra.

Quality is surprisingly good for 360p.

No need to go to school, learning online is enough., take an exam for grading.

@rajupowers

8 жыл бұрын

+Nikola Romanos it's basically the motivation factor. When you go to school, you spend money and time and so you try to get something out of it

@huihui666

8 жыл бұрын

+rajupowers Not just motivation, but also tradition factors. A degree earned by physically going to a university and study is regarded as more valuable to employers than a degree you obtained online. But in the future, this might change as technology evolves.

@rod-abreu

7 жыл бұрын

I wish I had access to something like internet when I was a kid, maybe I'd have had quit going to school, which was almost in vain, talking about math. The public education system in Brazil has collapsed for years :(

@logicboard7746

7 жыл бұрын

Exactly my thought

@webgpu

6 жыл бұрын

Rodrigo Abreu - kzread.info/dash/bejne/fpeuzqmEd5CnlZc.html

thanks it's helpful

shes is so sweet and a good teacher

I think there is an error at 7:55. The column space shouldn't have the axis labeled with a variable as the column vector is all the same variable. Strang, for instance, uses a no-variable axis. Thoughts?

Well explained.

Great!

Good Job Professor

I must say so like "BuddyNovinski" .Thank you so much.

perfect!

@jeevam7110

10 жыл бұрын

yes u right

Where was the first lecture? this was the first video in the playlist...?

it explanation well enough

MIT OCW is awesome!

Column picture part was good.

MIT的公开课都在youtube上吗