Lecture 2: Multiplying and Factoring Matrices

[@pikapuff123]

Before I went to grad school in the summer of 2015 I watched Dr. Strang's entire 18.06 course to make sure I was prepared. Now, five years later, PhD in hand, I still learn something every time I watch him speak.

[@nilbiescss2101]

Where i can find this course sir ?

[@allandogreat]

The same as you, Dr.Strang gave me a solid foundation for my PhD.

[@hanklin4633]

omg same, currently watching this before going to grad school!

[@jacobkoel5285]

Professor Strang is my new favorite person.

[@wyb314]

老教授实在是太伟大了，如此高龄居然还奋战在一线，太难得了！

[@allandogreat]

This senior professor is great indeed, it is too precious that he is working in teaching in his old age ^^

[@ADITYAMISHRA-g1p]

Thank you professor for this masterpiece.

[@raafeh9601]

Thank you Professor Gilbert Strang. That's the most clear lecture (and easy to understand), I have ever listened to on the web. You are a great teacher and know your material, providing great insights where needed.

[@swatisoni5818]

Best teacher of Linear Algebra ever!!

[@salehaboutaama7370]

God, I love this man!

[@arindam96]

I hope the content of this course and a few other DL courses enables me to make a superresolution version of 18.06 video. Man I love this guy

[@colin_hart]

I’m curious if you ever did this? I thought about it while going through 18.086 where recording is only available in 240p.

[@georgesadler7830]

DR. Strang thank you for a another awesome lecture on Multiplying and Factoring Matrices in linear algebra. I really enjoy this part of linear algebra.

[@warrenmarren4555]

Thank you Professor Gilbert Strang. FROM ALGERIA

[@mattiapennacchietti9224]

THANK YOU MIT

[@sakshisharma4165]

When he said " It's fantastic to have these beautiful clean boards". I was thinking the same. lol

[@अंशुमानअवस्थी]

notes kaise milen yr??

[@nowhereman8374]

Fyi just a small clarification to Professor Strang first equation on eigenvalue decomposition. In general, the decomposition is : A = QLamQ_inv which in the case of a symmetric matrix, S = QLamQ_trans. In this case: Q_inv = Q_trans. Thankyou Wolfram Math World and python

[@phamhongvinh550]

I really like the video quality. Thank you so much

[@SomenathRoyChoudhury]

Thank you Professor Gilbert Strang for your awesome presentation , got inspired to be faculty.

[@veeecos]

Increasing the speed to 1.5 to 2x makes this really interesting :)

[@GourangaRoy-m5c]

No

[@BigBen866]

Would have loved to have Professor Strang 40 years ago when I first experienced Linear Algebra in Pre-Algebra 1 and 2; 30 years ago in Finite Math with Calculus.

[@nganguyenviet152]

Thanks for your amazing course, professor Gilbert Strang! I really enjoy it.

[@iwtwb8]

This man just truly loves linear algebra, and it's fantastic.

[@sidolin6671]

Again prof you made my day!

[@allyourcode]

This course gives me an intense urge to raise my hand with the answer to the professor's questions!! (Ofc, unlike the live audience, I have the benefit of the pause button :P)

[@ronhernandez8857]

such a charming fellow

[@MauTaRe]

Thanks for these lectures and for the effort in putting together these videos!

[@RC-bm9mf]

39:03 typo in subtitle, “only r genuine independent equations...” should be right, not “are” in place of “r”. Thanks a lot!!

[@koushik7604]

You are just amazing sir 🙏

[@dauletbaimagamabet]

Gilbert Strang is so cool, thank you!

[@zakariabelgoum7850]

Such a lovely human being.

[@junyan6445]

Great improvement on video quality compared with 18.06

[@chaoticoli09]

How are the students getting picked up on the microphone? I think that it is neat as it is usually difficult to hear the students’ questions.

[@吴国豪-r2y]

In 26:47, Is there any relation between L U and L1 U1 L2 U2?

[@yuchenzhao6411]

I don't know what do you mean relation. L1 and L2 are first and second column of L, U1^t and U2^t are first and second row of U. I think the example he gave is just to give us a new way (column times row) to think about matrix multiplication (L times U) and how is it related to elimination.

[@xiaoqiangliu4384]

Great illustration

[@ThemJazzyBeats]

When Professor Strang breaks down the S matrix around the 11 min mark, can those qqT be considered as sort of ''basis vectors'' of a vector space who's elements are matrices ? The way I interpret the developpement of S around 11 min is that of a linear combination of qqT's and the scalars of the linear combination are the eigenvalues. I am sort of assuming that since Q is orthogonal, all of the qqT's will also be ''orthogonal'', although I'm not quite sure how to show that 2 matrices are orthogonal to each other.

[@jitheshdsouza98]

I suppose you can. You are basically adding bunch of rank1 matrices to get original rank n matrix. But space is described by vectors. Matrix describe linear transformation.

[@chonnyung5084]

Great lecture- thanks

[@hassanshka6711]

why did he make the columns space equal to m rather than n i didnt't understand isn't supposed to column space is equal or less than the number of columns in the matrix. he wrote the column space to be the number of rows dimension 38:04

[@taylorlorenztransormation3102]

Anyone know where homework solutions are found?

[@baobaolong423]

after 10 years, I still cannot clearly understand why the dimension of the null space is n-r...

[@RecklezzMusic]

If by r you mean rank, then it's quite clear. The dimensions of the null space are the number of columns with free variables. As such, n for the total number of columns minus, the rank, which is the number of pivots (independent variables). The proof is: nul(A) + rank(A) = n, shift it around and you get the above. =D I hope it helps

[@darkbrain2809]

intuitive-math.club/linear-algebra/null-space helped me a lot. Maybe review 1-11 which helped with visualizing matrices as transformations

[@henrmota]

If you see a matrix as a column space of transformation the null space are all the non zero vectors that land at zero after the transformation

[@kodyamour6330]

That first lecture had hundreds of thousands of views. This one has less than 100,000 still. Let's see how many views there will be in lecture 30 lol

[@ilyaphilippov7073]

Lectures are super useful. Are there any answers to the assignments if I ma not enrolled to the MIT?

[@mitocw]

No, sorry. Solutions were not provided for the problem sets.

[@seventyfive7597]

Traditional camera angles were WAY easier on the eye.

[@Enerdzizer]

In LU decomposition he assumed that l1*u1 will cancel first column of A. And he took u1 as the first row of A. But what if the first row of A have first element as zero.

[@Enerdzizer]

I figured out. Just take second or any other row with nonzero first element

[@manoranjansahu7161]

Better than it's 18.06 counterpart

[@diewunderschonelayla8426]

EEiigenväktoars. Ich liebe es

[@muhammadusman-pc3on]

Can we have access to programming assignments made for this course?

[@ludovicacastracane4975]

Dear Prof. I was wondering if you can solve for me this simple equation: 35x11 3+5 385 = Many thanks, L

[@TSCforThomas]

This is amazing........

[@nishensemble]

"I'm coming" - Mr. Cognitive Decline "Not today" - Dr. Strang

[@naterojas9272]

How much MIT must one do to be eligible for a Brass Rat?

[@koushik7604]

Couldn't understand why people are disliking?

[@jettdormitorio8555]

🐐

[@SSNewberry]

WWSD? (What would Strang Do?)

[@itachi4alltime]

these operations it's like wizardry

[@戴贤文]

where can i find the answer of problem sets？

[@guangleiwang2114]

Legend.

[@goldplatealuminum1102]

Nice

[@JoyTheDataScientist]

So he's saying we can email him our homework problems?

[@mitocw]

Just in case you are not joking... please do not email him your homework problems. K thx bye. :)

[@RC-bm9mf]

I guess he says about what the reader of the book he wrote did according to the preface - to send him interesting question (to enrich the next edition of the book). That’s why people do so.

[@phuongnamphan335]

where is the online homework ?

[@Mathin3D]

I liked this vid the moment I clicked on it.

[@aimaniac3919]

Did not quite understand @37:55, why we have three elements [ - - - ] in matrix size = 2 , Kindly help if someone understood

[@jefthervieira1]

"The simmetrical is the king of the matrices and the Orthonormal the Queen"... and the Queen and her twin sister get together with their greek lover(*beat starts at background*) listening Isaac Hayes and... wait! what we're talking again?

[@SphereofTime]

17:26

[@muhammadwahaj1712]

Anybody studying this course nowadays? I need some help

[@muhammadwahaj1712]

@ddanncppoli chi why did you say this?

[@osamaelgendy7807]

could someone please tell me which videos exactly have the signal processing part, because I studied a lot of that content already and I'm here for computer vision purposes

[@mitocw]

Are you looking for something like this? 6.801 Machine Vision, Fall 2020: ocw.mit.edu/courses/6-801-machine-vision-fall-2020. We hope this helps you!

[@osamaelgendy7807]

@@mitocw this course doesn't contain image processing, so I guess there is no signal processing as well

[@mitocw]

The 18.065 videos focus on the math frequently used in signal processing. Just the math not the application. Maybe this course is a better match for what you are looking for: ocw.mit.edu/courses/6-003-signals-and-systems-fall-2011/. Best wishes on your studies!

[@osamaelgendy7807]

@@mitocw Thanks a lot ❤️

[@KipIngram]

5:08 - Therefore, every King should have his two Queens. ;-) Totally logical to me. Or perhaps Q is the queen that's a lady by day, and Q-transpose is the queen who's on her back. :-| Sorry guys - couldn't resist.

[@husseinfg1478]

there is a special place named hell for ppl who disliked this video

[@godfreypigott]

Alas, there is no such place.

[@toddmarshall7573]

Does this guy realize how bad a teacher he is? KOIK abounds.

[@Avicenna10]

I hope that was a joke. Dr. Strang is AMAZING. If you think he's a bad teacher, you haven't been around much. I would have given almost anything to have had him as an instructor back in my college days.

[@toddmarshall7573]

@@Avicenna10 no. It wasn't a joke. I had more professors like this than I had good ones. One thing that abounds with these type of instructors. COIK: clear only if known. Just review the videos and observe how many times he starts a explanation and doesn't finish it. it's finished in his head but not with his class. If they're expected to be able to finish it they don't need to be taking the class... He doesn't need to start saying it in the first place. This is not idle criticism... it's crucial to good teaching

[@lee_land_y69]

Todd Marshall you need to watch 18.06 lectures before this, it’s assumed you know the contents of his previous course. If you have your bases covered, his explanations are 100% comprehensive. He doesn’t explain all the little details, because students know what he’s talking about and this is a review.

[@toddmarshall7573]

@@lee_land_y69 you need to understand what I wrote. I know this subject. I had professors like this. I got far more out of schaum's outlines than I ever got from this type of teaching. Watching it going on 50 years later it still disgusts me.

[@lee_land_y69]

Todd Marshall, well I don’t know your experiences. Just kinda surprised to hear someone’s unhappy with strangs teaching.

[@SphereofTime]

30:19