Lecture 1: The Column Space of A Contains All Vectors Ax

Рет қаралды 318,133

5 жыл бұрын

MIT 18.065 Matrix Methods in Data Analysis, Signal Processing, and Machine Learning, Spring 2018
Instructor: Gilbert Strang
View the complete course: ocw.mit.edu/18-065S18
KZfaq Playlist: • MIT 18.065 Matrix Meth...
In this first lecture, Professor Strang introduces the linear algebra principles critical for understanding the content of the course. In particular, matrix-vector multiplication Ax and the column space of a matrix and the rank.
License: Creative Commons BY-NC-SA
More information at ocw.mit.edu/terms
More courses at ocw.mit.edu

Пікірлер: 270

@tchappyha4034 5 жыл бұрын

The greatest math teacher in the world now teaches Data analysis, Signal Processing and Machine Learning! Thank you very much!

@frankbreeze9895 5 жыл бұрын

I cannnot agree with you more. I think hundreds of thousands of people have benefited from this great teacher!

@colinmaharaj 4 жыл бұрын

@@frankbreeze9895 That means you can agree with him more :)

@guohaodu5713 4 жыл бұрын

@@frankbreeze9895 that's right!

@piotrek0207 3 жыл бұрын

Right :)

@_nttai 3 жыл бұрын

I can't believe I'm watching this for entertainment at my own will. He's probably the greatest math teacher I've ever had

@xeneseken 5 жыл бұрын

It is snowing at the outside at 4:58. what a wonderful and lovely class.

@vikranttyagiRN 5 жыл бұрын

So beautiful.

@niknenkov3667 5 жыл бұрын

nice to notice that

@gongfei 5 жыл бұрын

focus, dude, focus!

@muzammil2587 5 жыл бұрын

it was so distracting!

@martinds93 4 жыл бұрын

40°c Outside my house right now.... And me, looking at this, is like torture.

@TheFrygar 5 жыл бұрын

omg it's snowing outside and these kids are sitting in a nice cozy room listening to one of the greatest linear algebra teachers in the world...I think I could die happy after such an experience

@jerrymahone335 5 жыл бұрын

Dr. Strang is a national treasure.

@ekbastu 4 жыл бұрын

international

@RC-bm9mf 4 жыл бұрын

Universal, I mean, literally in the universe.

@senwang1982 3 жыл бұрын

human's treasure

@vithaln7646 3 жыл бұрын

may be universal , entire world watch him

@wibirama 4 жыл бұрын

Prof. Gilbert Strang's videos had helped me during my M.Eng. study, I watched him once again in 2011-2014 during my PhD. Last year I got his new book, and today I am watching (again) he is teaching linear algebra for data analysis, signal processing and machine learning because I have to teach Fundamentals of AI for my undergrad students. Thank you so much Prof. Strang, you are my best online mentor in mathematics!

@kavanavvasishta4692 5 жыл бұрын

I was just watching his 2005 video lectures of Linear Algebra and I suddenly got to this lecture. I don't know why but it broke my heart to see Prof. Strang aged so much. Such a lovely human!

@cutieFAIZANHASSAN 4 жыл бұрын

same.

@aayushkumar6955 4 жыл бұрын

@Hotheaddragon 4 жыл бұрын

Same here

@akash.deblanq 3 жыл бұрын

@flowersunny7966 3 жыл бұрын

He's living a good life.

@jonahansen 5 жыл бұрын

Gotta hand it to Dr. Strang! He's still going strong and loves doing it. Those students and all viewers of these videos should consider themselves lucky...

@zkhandwala 5 жыл бұрын

At 84 years of age, he continues to be a maverick in the world of math education. Inspiring, to say the least.

@jdoesmath2065 2 жыл бұрын

As someone who has studied mathematics for 40 years and taught mathematics for 30 years, I can say that Professor Strang's wisdom and insight is amazing. Moreover, his ability to share this insight with enthusiasm (however quirky and geeky) is a gift to all of us. Thank you Sir. Bless all those dedicated to teaching.

@tcveatch Жыл бұрын

I like the feeling of watching the snow come down as we learn the comfortable and warm truth of things, in a safe kind classroom where careful work brings predictable success. The earnest student has faith that study will indeed bring learning, despite the cold and snowy world outside.

@javiervalenciagoujon5888 5 жыл бұрын

The best linear algebra teacher in the world now is going to teach us how to apply this concepts in real world problems . I can't thank enough MIT OCW and professor Strang for this.

@Zonnymaka 5 жыл бұрын

24:38 16*(first row) -9* (second row)= (third row) Welcome back Doc Strang!

@allergictoalliteration6033 6 ай бұрын

Thank you! How do you derive it? Is it just through trial-and-error with different combinations? Or is there a better/more intuitive approach?

@Zonnymaka 6 ай бұрын

@@allergictoalliteration6033 Just take the first 2 rows and turn them into 2 columns (call the resulting (3x2) matrix A). Then solve Ax=b where b is the third row turned into a (3x1) vector.

@jen-lichen8163 5 жыл бұрын

With this awesome tutorial and maybe one of the most passionate professors I've ever seen, even the snow outside the window seems to show some Christmas feelings.

@ecapanema 2 жыл бұрын

This Professor is simply amazing. So humble to teach and so thorough. Thanks for this!

@gongfei 5 жыл бұрын

4:42 A multiply x, matrix A times vector x, how to look at that, think of the *rows* , combination of the vectors 8:56 column space of A, C(A) 18:31 C: the basis of A's column space 20:00 the column rank of A 20:22 A= C times R, factoring 23:49 column rank = row rank

@Shulkyl 4 жыл бұрын

🙏

@zrmsraggot 2 жыл бұрын

9:05 ?

@pranayc94 4 жыл бұрын

It’s so refreshing to see Prof.Strang teaching again. Man what an exiting adventure.

@gabriellaugusto 5 жыл бұрын

Finally this course has been release in MIT OCW! Thank a lot!

@semtex6412 Жыл бұрын

who else is here to reminisce the past with this awesome professor? 66 years of MIT!

@user-ef3ej4pq4f 5 жыл бұрын

Although I have learnt Linear Algebra in last semester, Still feeling refreshed and amazed watching these lectures, Dr. Strang's teaching skill is sooo good!!!

@dennisestenson7820 2 жыл бұрын

I watched his 18.06 lectures online in the mid 2000's and it left a deep impression on me. I am so happy to see he's still teaching and share his excitement about him teaching this course.

@saratbhargavachinni5544 5 жыл бұрын

Very excited to learn one more Video course from Prof Gilbert Strang, One of the best teachers I have ever had!!

@user-uq7ri1pz2c 3 жыл бұрын

Gilbert Strang, thank you very much for everything you have done for us. You are the best teacher I have ever met

@seamus9898 5 жыл бұрын

Glad to see he's well! Much better than the 240p quality of the original linear algebra videos.

@raitup00 5 жыл бұрын

Agree! What a difference!

@victorsung3582 5 жыл бұрын

The content in his original lectures are still amazing! :)

@gongfei 5 жыл бұрын

@@victorsung3582 the video resolution doesn't matter at all.

@deeprecce9852 5 жыл бұрын

Absolutely delightful to see another of Prof Strang lectures..., PS A busy and working minds is like a brain exercise that will keep you mentally healthy for a long long time!!

@xingjieli3069 2 жыл бұрын

It's great to revisit all linear algebra from a different point view! It really opens my mind! Thank you Professor Strang!

@avizzzzzzzz Жыл бұрын

Prof. Strang is a magician. the way he pulls out tricks from his hat and makes sound Linear Algebra concepts fun to students. Respect Respect, only 75% through this video and mesmerized. Charismatic teacher. raw suave, trickery from the magician teacher.

@arvindkumar2174 5 жыл бұрын

Thank You very prof. strang for this lectures. I always thought if prof. strang would have taught this lectures then it would be the best. Now we have this. Now I will get up early and my first task will be to complete prof. strang lectures. Thank You very much professor. Be healthy and long live.

@basit005 5 жыл бұрын

I got his linear algebra book in 2011, never really finished it as I had graduated and got into different things. Out of curiosity I started this video, it seems like Strang's hands are shaking and twitchy. I didn't realize he had gotten this frail and old, but its interesting to see that the mind is still as sharp as a razor edge. He has done a lot with his life and I hope that people who watch this lecture series go on to carry his legacy when he isn't around any more :')

@yanfengliu 5 жыл бұрын

Wow all the concepts make so much more sense now. Dr. Strang really is a great teacher!

@alexandrefelicio3902 4 жыл бұрын

Professor Strang is absolutely amazing! The best math teacher I have ever seen!

@madmanzila 5 жыл бұрын

Much respect To Professor Gilbert Stang.

@BleachWizz 3 жыл бұрын

27:00 To find the combination you're going to scale the first one by a and the second one by b, then try to find c: From first column: 2a+3b=5 From second column: a+b=7 Working on first: 2(7-b)+3b=5 b=5-14=-9 Working on second: a=7-(-9)=16 So: 16.r1 - 9.r2 = r3

@apetrenko_ai 2 жыл бұрын

Thank you, was looking for this comment!🙂

@CardiganBear Жыл бұрын

Or, find the reduced row echelon form of the transpose matrix = [1 0 16, 0 1 -9, 0 0 0]. Tells you that you need 16 of col 1 (originally row 1) minus 9 of col 2 (row 2) to make col 3 (row 3).

@skilambi 5 ай бұрын

He's a realized soul!!! Not less than a saint. How many people have benefitted from this great mind! I cannot thank him enough.

@jamesgoodman2641 5 жыл бұрын

I am convinced that MIT 18.065 is one of the best math courses in the world. There is no exaggeration to say that it serves as the mathematical enlightenment to me thanks Dr Strang

@romanbesel4759 3 жыл бұрын

Absolutely fantastic! Such a pleasure to learn about this interesting topic by a gifted teacher like Gilbert Strang.

@amruthgadag4813 3 жыл бұрын

A mesmerizing amazing person ever. I am really astonished to see his dedication to linear algebra. A big salute to him.

@IrfanAli-mo6mh 5 жыл бұрын

Thanks for opencaourseware that we can learn from this legend of Linear Algebra....

@valentinussofa4135 2 жыл бұрын

Maybe I don't have basic in Mathematics, but when I read Prof Strang books about linear algebra (all deep learning for my dream project in machine learning). And now I introduced to Prof Strang OpenCourse, I'm feeling blessed and inspired as Computer Programmer Learner. Thanks to MIT & Prof Strang from East Nusa Tenggara Province, Indonesia. 🙏🙏🙏

@realworld8690 4 жыл бұрын

Following his lectures since 2017, greatest teacher .

@MichaelKim505 5 жыл бұрын

Thank you for the video lectures Prof. Gilbert Strang, I learned a lot from them.

@salimmiloudi4472 5 жыл бұрын

Thank you very much Prof. Gilbert Strang, you're awesome as always :))

@eshwarray3993 4 жыл бұрын

You are the god of Maths.Thank you for making such videos. Most maths teachers know maths but they dont know how to teach maths.You teach in such a way which could be understood by even a high school student.thanks a lot

@kristiantorres1080 4 жыл бұрын

Thank you MIT for making these lectures public!

@AdityaSharma-do1ho 3 жыл бұрын

God bless Dr. Strang! There are Innumerable people in the STEM fields who owe their careers to stalwarts like him. A human treasure of knowledge!!

@piotrek0207 3 жыл бұрын

Thank you MIT OCW for sharing knowledge.

@res0nanc320 5 жыл бұрын

So happy to see Professor Strang still teaching beautifully. Even more happy that he’s mentioned Julia already in lecture 1. Thank you MIT for providing such up to date material.

@robertcummings952 5 жыл бұрын

1q11q11q1qq1q1q1q111q111qqq1111q11q11q1qqq1111111111q11111q1111q11qq111qqq1q111qq11q11q111112q11111q1q1q11q1q1q1q1111111111q1111q111q1q1q1q11q1q111q21111q11111q1qq111q2q1*1212q1221112111q1wwawwweawp

@ozankaya1061 3 жыл бұрын

I stumbled upon this playlist and it really made my day. This is so good.

@junyan6445 5 жыл бұрын

I really respect Prof. Gilbert Strang!

@georgesadler7830 2 жыл бұрын

DR. Strang thank you for a fantastic lecture to start this new class for MIT and all students in mathematics.

@izreeljames7953 2 жыл бұрын

I am grateful for utilizing your gift masterfully ^ beautifully. Thank you Mr. Gilbert Strang!!

@kellypainter7625 5 жыл бұрын

Prof. Strang is such a good teacher. Awesome.

@zainabedien6674 5 жыл бұрын

i HAVE FAST TODAY. I really dont want to do any thing but i started your lecture and just get busy in dimensions. kudos to you Sir. you are my mood changer.

@JaGWiREE 5 жыл бұрын

Thank you so much for releasing this course :).

@plaustrarius 5 жыл бұрын

This is amazing! Just found out about this and I am so excited!!!

@EvanZamir 5 жыл бұрын

Thank you for these lectures, Dr. Strang.

@davidorr947 5 жыл бұрын

Clearly the best teacher on the planet!

@tdchayes 5 жыл бұрын

24:00 The combination of rows is 16*row1-9*row2-row3=0

@rashidissa5887 4 ай бұрын

I don't understand anything here, but I'm fascinated watching you,Sir. I only have an O-Level maths (1967) Cambridge but still following up lessons in the U-tube for the love of the subject

@kikirizki4318 5 жыл бұрын

You are amazing mr Strang. Give me deeper understanding about machine learning

@reneeliu6676 5 жыл бұрын

Thank you Professor Strang! I am going to get up early tomorrow morning and watch this video with the best part of my day! I also need to buy a super expensive notebook only for Professor Strang's class!

@happyhappy-dg2fy 4 жыл бұрын

hahaha, me too

@Muxik4k 4 жыл бұрын

Renee Liu why expensive?

@pfever 5 жыл бұрын

You have to love MIT! Thank you! :)

@sajalmukhopadhyay9695 5 жыл бұрын

You are our inspiration. This is amazing.

@arnoldbr8418 2 жыл бұрын

I love this man, for he, by showing the meaning and relations, makes me love Linear Algebra, a subject that used to bother me.

@ercanboztepe4468 5 жыл бұрын

Thanks legend!!! This course is a key of machine learning area.

@StewieGriffin 4 жыл бұрын

A very clear spoken professor. I learned a new word. "Bashful" just from the context he used the word in. I assumed Bashful meant shy because he asked the students that were bashful to sit far back. Which indicates the word "shy" as in the term "camera-shy".

@malyabanbal6738 5 жыл бұрын

great course...was waiting for it for a long time!! :)

@vivianhsu7334 5 жыл бұрын

Thank you Dr. Gilbert, you made me fall in love with math,I hope everything is well.❤️🍀

@hj-core 10 ай бұрын

Come from 18.06 tape. Happy to learn from professor strang again🎉

@abdulrahmansattar2873 5 жыл бұрын

Thanks MIT And Prof . Gilbert Strang!

@soul2180 3 жыл бұрын

Extraordinary intellect and brilliant math professor

@jielin6467 5 жыл бұрын

Thank you for the lecture series!

@kevintoner6068 3 жыл бұрын

After watching his earlier lectures it feels strang(e) to watch him in such high quality

@al3xg.0 4 жыл бұрын

Professor Strang is an absolute legend!

@magno5157 5 жыл бұрын

If there's only one thing to take away from Strang's lectures/lessons, it is this (which he emphasizes in one of his textbooks): Understand in depth the four most fundamental subspaces: the row space, the nullspace, the column space, and the left nullspace.

@Sahil_Love_416 5 жыл бұрын

Not even a single dislike , that's Gilbert strang for you

@grjesus9979 4 жыл бұрын

That's what I call a good teacher!

@yuc.w.1217 4 жыл бұрын

Thank you, Dr. Strang.

@alileo1578 4 жыл бұрын

That it is snowing outside makes everything even better :))

@allandogreat 5 жыл бұрын

It will be such honor to sit there to listen Mr Strang’s lectures

@allandogreat 2 жыл бұрын

Come back and study it again, you still can get some new.

@plekkchand 3 жыл бұрын

Glad the intro properly says "high quality" rather than the illiterate "quality" so often used now to describe the video which follows.. At least there is one place left which respects language. MIT is to be commended for this alone.

@MuhammadGhufran5 5 жыл бұрын

Thank u very much Prof. Strang !

@hankigoe829 2 жыл бұрын

it feels great to be getting in on the ground floor of the singularity

@alexkudzin4980 4 жыл бұрын

first row (2 and 1) multiply by 16 ( 32 and 16) second row (3 and 1) multiply by -9 (-27 and -9) then add the two rows ( 5 and 7) (or subtract if you multiplied by 9)

@flatbreadthom 3 жыл бұрын

He reminds me of Jimmy Stewart. Very unassuming. Makes out as though he's figuring it out as he goes along, but of course he wrote the book. Zen master at work!

@henrmota 4 жыл бұрын

I would love to have this man as my teacher.

@Saerwon 5 жыл бұрын

Best professor ever.

@nicholasjaramillo9561 5 жыл бұрын

I LOVE THIS GUY!!! AWESOME TEACHER

@mohammedtarek9544 3 жыл бұрын

i have finished 18.06 and i thought that i wont see professor gilbert and the infinite black black board together in a video again pretty happy :D

@Muxik4k 4 жыл бұрын

The best professor.. ever!! 😊👍🏼

@germantuto6637 4 жыл бұрын

Muy buena explicación, que buen curso.

@xy-xe4zl 5 жыл бұрын

long time no see, dr.strang! 2year ago i watched linear agebra vedio

@JonasNgYF Жыл бұрын

I accidentally clicked into this, and watched it. I was supposed to watch Yoona's Big Mouth on Disney+. Thanks Prof Strang for the knowledge.

@lianjunmei424 5 жыл бұрын

thank you, professor strang

@RC-bm9mf 4 жыл бұрын

33:52 Professor Strang hasn’t taught the 18.06 for a while and he observes the lectures these days at MIT are taught in a very abstract way, unlike how he presented concepts such a column space 20 years ago. That’s why he said what’s going on? So the ‘range’ terminology of these days is the same as our good friend C(A)!

@RC-bm9mf Жыл бұрын

I watched this again! ❤