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

[@tchappyha4034]

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

[@frankbreeze9895]

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

[@colinmaharaj]

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

[@guohaodu5713]

@@frankbreeze9895 that's right!

[@piotrek0207]

Right :)

[@_nttai]

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

[@kavanavvasishta4692]

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]

same.

[@aayushkumar6955]

:(

[@Hotheaddragon]

Same here

[@a1x45h]

:(

[@piotrek0207]

Same thought

[@TheFrygar]

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

[@xeneseken]

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

[@vikranttyagiRN]

So beautiful.

[@niknenkov3667]

nice to notice that

[@gongfei]

focus, dude, focus!

[@muzammil2587]

it was so distracting!

[@martinds93]

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

[@wibirama]

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!

[@jerrymahone335]

Dr. Strang is a national treasure.

[@ekbastu]

international

[@RC-bm9mf]

Universal, I mean, literally in the universe.

[@senwang1982]

human's treasure

[@vithaln7646]

may be universal , entire world watch him

[@tcveatch]

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.

[@zkhandwala]

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

[@skilambi]

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

[@Zonnymaka]

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

[@allergictoalliteration6033]

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]

@@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.

[@jonahansen]

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...

[@AnhTran-sf3hf]

There was a special feeling in me when I saw him at this age still giving out great lectures. I can see he is not as strong as in 1806 but the way he teaches is still super powerful.

[@javiervalenciagoujon5888]

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.

[@jdoesmath2065]

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.

[@gongfei]

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]

🙏

[@zrmsraggot]

9:05 ?

[@BleachWizz]

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]

Thank you, was looking for this comment!🙂

[@CardiganBear]

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).

[@valentinussofa4135]

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. 🙏🙏🙏

[@avizzzzzzzz]

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.

[@AdityaSharma-do1ho]

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!!

[@dennisestenson7820]

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.

[@jamesgoodman2641]

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

[@res0nanc320]

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]

1q11q11q1qq1q1q1q111q111qqq1111q11q11q1qqq1111111111q11111q1111q11qq111qqq1q111qq11q11q111112q11111q1q1q11q1q1q1q1111111111q1111q111q1q1q1q11q1q111q21111q11111q1qq111q2q1*1212q1221112111q1wwawwweawp

[@LowLifeGraphicsProgrammer]

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!!!

[@IrfanAli-mo6mh]

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

[@ВадимШатов-з2й]

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

[@basit005]

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 :')

[@madmanzila]

Much respect To Professor Gilbert Stang.

[@arvindkumar2174]

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.

[@eshwarray3993]

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

[@seamus9898]

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

[@raitup00]

Agree! What a difference!

[@victorsung3582]

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

[@gongfei]

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

[@tdchayes]

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

[@ecapanema]

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

[@iwonakozlowska6134]

24:44 system: 2a+3b=5 , 1a+1b=7 solution: a=16 , b=-9

[@deeprecce9852]

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!!

[@reneeliu6676]

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]

hahaha, me too

[@Muxik4k]

Renee Liu why expensive?

[@zainabedien6674]

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.

[@semtex6412]

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

[@kristiantorres1080]

Thank you MIT for making these lectures public!

[@piotrek0207]

Thank you MIT OCW for sharing knowledge.

[@gabriellaugusto]

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

[@pranayc94]

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

[@jen-lichen8163]

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.

[@amruthgadag4813]

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

[@realworld8690]

Following his lectures since 2017, greatest teacher .

[@rashidissa5887]

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

[@seraphimwang]

43:50 The moment one realise that he is the 😎 and everyone has so much respect for such as beautiful soul. I would be honoured to be one of his ‘pupil’ student or assistant. A 🎩 to a unique gentleman!

[@plekkchand]

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.

[@soul2180]

Extraordinary intellect and brilliant math professor

[@StewieGriffin]

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".

[@alexkudzin4980]

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)

[@nutzer5714]

This course is the reason why I took the numerics course at my Uni

[@saratbhargavachinni5544]

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

[@arnoldbr8418]

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

[@alexandrefelicio3902]

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

[@davidorr947]

Clearly the best teacher on the planet!

[@yanfengliu]

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

[@flatbreadthom]

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!

[@junyan6445]

I really respect Prof. Gilbert Strang!

[@kellypainter7625]

Prof. Strang is such a good teacher. Awesome.

[@xingjieli3069]

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

[@RC-bm9mf]

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]

I watched this again! ❤

[@SphereofTime]

11:42 column space is line, rank is 1

[@Sahil_Love_416]

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

[@vivianhsu7334]

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

[@izreeljames7953]

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

[@hj-core]

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

[@magno5157]

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.

[@allandogreat]

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

[@allandogreat]

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

[@SphereofTime]

5:00 First Matrix - 44:00

[@romanbesel4759]

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

[@georgesadler7830]

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

[@MichaelKim505]

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

[@salim.miloudi]

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

[@kadenabet]

The discrepency from canadian universities to MIT is an order of magnitude w.r.t to quality. I am so thankful M.I.T did this.

[@ozankaya1061]

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

[@hankigoe829]

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

[@grjesus9979]

That's what I call a good teacher!

[@Tggfredcsawsdfgbhhhhu]

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

[@kikirizki4318]

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

[@al3xg.0]

Professor Strang is an absolute legend!

[@alileo1578]

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

[@mohammedtarek9544]

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

[@sajalmukhopadhyay9695]

You are our inspiration. This is amazing.

[@pfever]

You have to love MIT! Thank you! :)

[@jacekc6179]

Fantastic weather outside. Snow!

[@heidioid]

Bookmark, random sampling of matrix 36:20

[@JaGWiREE]

Thank you so much for releasing this course :).

[@taylorlorenztransormation3102]

Can someone help me? Around 30:0 to 33:33 I don’t understand that multiplication. To me it doesn’t look the A matrix is equal to the transposed matrix times the identity matrix. One time zero is zero. Not one. (From top row of second column)

[@ercanboztepe4468]

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

[@ryanwwest]

40:37 "I got excited thinking about math". Best

[@plaustrarius]

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

[@Saerwon]

Best professor ever.

[@EvanZamir]

Thank you for these lectures, Dr. Strang.

[@emptyjns]

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.

[@aneesurrehmanasra9267]

Thank you #MitOpencrouseware. Live long professor strang. lots of love and respect from Pakistan.

[@muazahmetsalem5316]

you have to respect this man 🙏

[@jiang5240]

muath salem Absolutely

[@henrmota]

I would love to have this man as my teacher.

[@roy1660]

At 25:03 the row rank of the matrix can be found by converting the matrix A in echolon form. The reduced matrix will look like this 1 0 1 0 1 1 0 0 0

[@leatiletmarata3481]

If i had some powers vested in me, I would declare him the greatest teacher of all times.