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

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

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

[_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

[tchappyha]

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

[xeneseken]

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

[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

[kavanavvasishta]

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!

[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!

[Zonnymaka]

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

[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...

[zkhandwala]

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

[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.

[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.

[jdoesmath]

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.

[javiervalenciagoujon]

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.

[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

[valentinussofa]

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. 🙏🙏🙏

[AdityaSharma-doho]

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!!

[dennisestenson]

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. <3

[jamesgoodman]

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

[basit]

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 :')

[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.