Lecture 2: Multiplying and Factoring Matrices

MIT 18.065 Matrix Methods in Data Analysis, Signal Processing, and Machine Learning, Spring 2018
Instructor: Gilbert Strang

Multiplying and factoring matrices are the topics of this lecture. Professor Strang reviews multiplying columns by rows: AB = sum of rank one matrices. He also introduces the five most important factorizations.

License: Creative Commons BY-NC-SA

[pikapuff]

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.

[jacobkoel]

Professor Strang is my new favorite person.

[raafeh]

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.

[ADITYAMISHRA-gp]

Thank you professor for this masterpiece.

[arindam]

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

[georgesadler]

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.

[iwtwb]

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

[sakshisharma]

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

[吴国豪-ry]

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

[nowhereman]

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

[phamhongvinh]

I really like the video quality. Thank you so much

[warrenmarren]

Thank you Professor Gilbert Strang. FROM ALGERIA

[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)

[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 :)

[RC-bmmf]

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

[nganguyenviet]

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

[BigBen]

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.

[MauTaRe]

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

[hassanshka]

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