
Gilbert Strang Teaches Linear Algebra - ColinWright
https://ocw.mit.edu/courses/mathematics/18-06-linear-algebra-spring-2010/video-lectures/
======
randomstring
I wish I had this when I was learning Linear Algebra. When it was taught to
me, both in HS and College, there was not a word of motivation about why we
were juggling numbers around in boxes. It was tedious and had seemed to have
no connection to anything.

I developed a strong dislike for LA, if not outright fear and hatred. This
from someone who majored in math at university. I later learned from reading
Dr Oakley's book, _A Mind For Numbers_, that this is a perfect recipe for not
mastering a subject. I was sabotaging my own learning by approaching it from
the point of view of something to be despised. It was many years later after
reading Oakley's book that I challenged myself to learn Linear Algebra.

I found the Coursera course Coding the Matrix
[https://codingthematrix.com/](https://codingthematrix.com/) perfect. Not only
did Professor Philip Klein explain the subject well, but it was also a
programming course in python. Coding the algorithms helped make them that much
more concrete. I'm happy to say I finished the online course with 100% grade.

Unfortunately Coding the Matrix is no longer available on Coursera.

I know this thread is more about Strang being a teaching god, and he is. I
wanted to add something on alternative ways to learn linear algebra.

~~~
ofrzeta
This is a problem I always had in university. Higher math always seemed to
start with "the definition of X is Z etc." and I would never know what's the
purpose of doing this. When I attended a talk of Gilbert Strang many years
later it was eye opening because it was a totally different approach that
always accompanied theoretical concepts with a concrete interpretation.

Actually I now think it might also be a cultural thing. If you take a look at
the approaches the English Wikipedia takes vs. the German Wikipedia take
explaining a vector space you'll know what I mean:

[https://en.wikipedia.org/wiki/Vector_space#Introduction_and_...](https://en.wikipedia.org/wiki/Vector_space#Introduction_and_definition)

[https://de.wikipedia.org/wiki/Vektorraum#Definition](https://de.wikipedia.org/wiki/Vektorraum#Definition)

~~~
big_chungus
I'd second the point on different cultures doing it differently. One of my
profs once said he had a book written by two mathematicians, one German and
another Italian. It was fairly evident who had worked on which part. He also
mentioned that the "old style" German books would almost apologize if they
"had" to use just a few pictures to illustrate something.

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Gene_Parmesan
I used this course years ago while I was self-teaching CS, really great
course. MIT in general makes some awesome stuff available -- so awesome, it
helped this disgruntled lawyer get the hell out of law and into my dream
field.

I can't express strongly enough how appreciative I am to MIT, and also schools
like Stanford and Harvard, and Prof. Sedgewick from Princeton, for making
courses like this publicly available.

~~~
elliekelly
I’m also a (formerly disgruntled) lawyer eternally grateful to Stanford and
MIT for helping me escape. And like you, I cannot overstate my appreciation.
If anyone involved in these courses stumbles upon this thread - thank you.

~~~
simonebrunozzi
I've been on the other side (CS professor for two years, apparently students
really loved my work) - if you can, email them and tell them about your
appreciation. It's worth it.

I don't know about others, but in my case I had to put up with a lot of BS,
and "older" colleagues that were envious of my "performance" (annual feedback
reviews by students). These few emails (and two letters!!) went a long way for
me.

~~~
imranq
I will do that! OCW, and Princeton Coursera have enabled me to do far more
than I ever thought was possible as an immigrant kid.

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melling
He has another advanced Linear Algebra class:

[https://ocw.mit.edu/courses/mathematics/18-065-matrix-
method...](https://ocw.mit.edu/courses/mathematics/18-065-matrix-methods-in-
data-analysis-signal-processing-and-machine-learning-spring-2018/)

And this new book:

[https://www.amazon.com/Linear-Algebra-Learning-Gilbert-
Stran...](https://www.amazon.com/Linear-Algebra-Learning-Gilbert-
Strang/dp/0692196382/)

~~~
jacobolus
These lectures are really excellent.

Packed with insight that would otherwise take years to pick up piecemeal
elsewhere.

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arbitrage
Gilbert Strang got me through linear algebra in University. Fifteen or so
years later, I told my wife who went back to school as an older adult about
him. He got her through, too.

His teaching capability is so great, we ended up buying his textbook and using
that instead of the one assigned by her college. My wife ended up with the
best grades in the class, but not only that, ended up actually learning the
material and retaining it many years later. Her field is in no way related to
mathematics, but it would not be an exaggeration to say that she benefited
greatly from her maths exposure.

Linear algebra, heck yeah! Thank you, Dr. Strang.

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thearn4
Related note: Strang's essay on the imbalance in education in favor of
Calculus over Linear Algebra is (in my opinion at least) a great read, for
those interested in the pedagogy of mathematics.

[http://web.mit.edu/18.06/www/Essays/too-much-
calculus.pdf](http://web.mit.edu/18.06/www/Essays/too-much-calculus.pdf)

~~~
jimbokun
I think Strang's videos should also be used as examples of all around great
pedagogy, independent of the Linear Algebra content.

He does more with some chalk and a big black board than any modern courses
using fancy presentation technology.

~~~
abhgh
Definitely - I went through some of his lectures after I had read up on Linear
Algebra as part of a course (from [1]) and had used it in a bunch of
applications, but I still found the lectures worth going through if only
because his fantastic exposition helped me visualize things better.

[1]we followed Huffman-Kunze [https://www.amazon.com/Linear-Algebra-Kunze-
Hoffman/dp/93325...](https://www.amazon.com/Linear-Algebra-Kunze-
Hoffman/dp/9332550077)

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anonsivalley652
At a different college, I loved that class. It brought equations to within a
hair's breath of symbolic data for me in 1+ dimensional arrays. It was
absolutely essential for the honors chemistry/physics/compsci track.

I had an HP 48G calculator at the time that could do symbolic derivation and
all of the matrix decompositions. And if it didn't have a function, it was
easy to write your own in any of four (4) programming languages: symbolic user
programs (User-RPL), their compiled language (System-RPL), C or assembly. The
matrix editor looked exactly like a spreadsheet. What's cool about HP's Erable
(CAS) is, just short of being LISP/Scheme, everything was a value. Compiled
binaries could be pushed on the stack (RPN). Oh and programs could be copied
to other HP 48G/GX's with it's incredibly-powerful serial IR port. Some
ingenious soul figured out how to turn the calculator into a _learning_ IR
remote control with a library of preset manufacturer codes. (I once turned on
all the TVs in the lecture hall from the back of the class (15 m away) with my
calculator during lecture... and people freaked out. :D) People modded them
with 2-8x as much memory by chip stacking and wiring the enable pin and an
inverter to the processor. None of this 64KiB rubbish, 512KiB FTW. And if you
couldn't see parens in your 3 line equation, there's a graphical equation
editor. Finally, if you got bored of that, there's always the easter eggs with
the team's name in a solved crossword puzzle and grayscale pictures of them
(not like Tetris on an Agilent oscilloscope, but okay).

I preferred his competitor's book because it made sense to me, Anton's
_Elementary Linear Algebra, Applications Version_

His book is _Introduction to Linear Algebra._

------
dsiegel2275
Strang is an excellent teacher and this an effective course for coming up to
speed in Linear Algebra fundamentals.

I watched every lecture and did most of the homeworks a couple of summers ago
in preparation for taking grad ML courses at Carnegie Mellon (10-601 Intro and
10-605 Scalable ML). The foundations that I built from Strang's course were
essential to my success later.

~~~
s5ma6n
Exactly this. I also studied from his video lectures and I owe most of my
understanding of the topic to him. He has an amazing ability to intuitively
explain complex concepts step by step.

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ivan_ah
This is an excellent course. That's where I first learned about the "column
picture" of matrix multiplication... and this after 10+ using linear algebra
and teaching. Overall LA can be a complicated subject, but Strang does a good
job at making it seem like common sense.

For more linear algebra goodness, check out the 3Blue1Brown playlist, which
provides a lot of the important geometric intuition:
[https://www.youtube.com/playlist?list=PLZHQObOWTQDPD3MizzM2x...](https://www.youtube.com/playlist?list=PLZHQObOWTQDPD3MizzM2xVFitgF8hE_ab)

Another good book with visuals and manipulatives is
[http://immersivemath.com/ila/index.html](http://immersivemath.com/ila/index.html)

And this is a short tutorial that I wrote that summarizes some of the main
ideas of LA in just four pages:
[https://minireference.com/static/tutorials/linear_algebra_in...](https://minireference.com/static/tutorials/linear_algebra_in_4_pages.pdf)
You can print this and enjoy with your weekend coffee tomorrow. For bonus
points, you can also learn how to do LA using SymPy here
[https://github.com/minireference/sympytut_notebooks/blob/mas...](https://github.com/minireference/sympytut_notebooks/blob/master/notebooks/Linear-
algebra.ipynb)

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rkochman
G-Strang! I took this class in the fall of 1999, and I remember thinking it
was unusual that every lecture was being recorded. So cool to see it still
having an impact 20+ years later.

------
brendanw
Gilbert Strang got me through the more difficult of the two linear algebra
gatekeeper classes in University. I didn't go to class once after the first
week. I sent him a thank you email and he wrote a nice reply.

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alecdibble
These videos helped me immensely when I was getting my Electrical Engineering
degree. I didn't realize going into the degree a bulk of the coursework would
be focused around fourier/laplace transforms and linear algebra.

------
manthideaal
I am not able to wait for a video to explain something, I prefer to read
books. I don't know what is good about this teacher. Linear Algebra Done Right
is a good book. I am not able to appreciate Gilbert Strang style. But algebra
is easy to grasp if you are motivated and prepared for hard work. I recall he
stressed SVD. Once you are up on statistics SVD is a very useful tool, but I
find his style overly pragmatic, if you are able to read a book like Linear
Algebra Done Right you will appreciate what a non pragmatic style mean here.
Anyway this can be sour grapes, I would like my students to enjoy my lessons.
Algebra Done Right goal is that you can demonstrate and learn for facts and
proofs. GS book is about using the tools of linear algebra.

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zeroego
I'm a current CS student. I've heard that Linear Algebra is a worthwhile class
for students studying Computer Science. Yet, my program doesn't have it as a
requirement. Can anyone explain in broad terms if this course is something I
should consider taking anyways?

~~~
vkou
If you ever intend to have anything to do with machine learning, computer
graphics, or work for a quant firm[1], yes.

If you want to work on adtech, CRUD apps, or uber-but-for-catsitters startups,
probably not. I have been working on two out of the three for a decade, and in
all this time, I haven't had to use a lick of linear algebra.

From an academic standpoint, it's arguably a more useful course for your
general education than calculus (Which is a requirement for just about any
degree), but less useful than statistics.

[1] If you ever intend to work for a quant firm, you should probably take a
lot more math courses than just linear algebra.

~~~
dbmikus
Adtech does a lot of machine learning, so at least a surface level
understanding of linear algebra is useful there.

~~~
vkou
Of the ~100 people in my immediate work area who work on a large ads product,
about 4 of them do ML.

The overwhelming majority of adtech is like any other enterprise business -
building CRUD apps.

------
lordleft
Gilbert Strang has this lovely patrician, avuncular energy that puts me at
ease. I feel like he's as likely to pour me a cup of tea as he is to expound
on matrices. He feels less like an MIT professor and more like a shared
pedagogical treasure of our internet age.

------
lwb
I have always thought that the best way to learn linear algebra would involve
constant visualization and interaction on a computer.

My LA teacher in college told us that he visualized the left matrix in a
matrix multiplication flipping over and crashing down on top of the right
matrix. (or is that backwards?) The only way I learned things like vector
spaces and orthogonality was by visualizing them in my head, Bret-Victor
style.

In my totally unqualified opinion, there is a huge opportunity for a software
product that allows people to play with and explore mathematical concepts in a
visual and fun way.

~~~
mkl
> the left matrix in a matrix multiplication flipping over and crashing down
> on top of the right matrix. (or is that backwards?)

Both ways work. A row from the left matrix rotated 90° clockwise to line up
with the rows of the right matrix gives you the coefficients to use to combine
those rows into a row of the result matrix. Conversely, a column from the
right matrix rotated 90° anticlockwise to line up with the columns of the left
matrix gives you the coefficients to use to combine those columns into a
column of the result matrix.

I didn't fully understand that until I read Strang's book.

------
tombert
This course was a godsend for me.

Before I dropped out of FSU, I managed to rope myself into two math classes
(Complex Variables and Game Theory), both of which had a strict requirement of
Linear Algebra, which I hadn't taken.

I was a bit panicked because it was a bit too late to sign up for anything
else, and so I binged through this MIT course, and learned _just enough_ to
get permission from both the professors to still let me take the classes. It
definitely would have been _better_ to have taken linear algebra directly, but
having this as a resource was super valuable.

------
bcheung
I watched a few of the lectures in the past. I was really impressed with his
teaching skills but the quality of some of the videos was really bad it really
took away from the learning experience. Really wish there could be a
professionally recorded version of him.

------
dreamer7
Linear Algebra and it's Applications, a textbook by Gilbert Strang was the
most entertaining textbook I've ever perused in engineering.

He has a great sense of humour and keeps slipping jokes in unexpected places.

------
darkapex
I watched these lectures the summer before starting university as Linear
Algebra was one of the mandatory courses for the first semester.

These are by far the best lectures on Math/CS I've ever seen. Helped me A LOT.

------
kiterunner2346
Is there a text focusing on the known differences between the lower
dimensional spaces of 1-4 dimensions and the higher-dimensionality spaces
commonly used in DNN calculations?

~~~
funklute
You might have to be a bit more specific about what exactly you are asking,
but for example this paper and its references might be an interesting start:
[https://bib.dbvis.de/uploadedFiles/155.pdf](https://bib.dbvis.de/uploadedFiles/155.pdf)

------
ssouris
I learned from his videos almost 10 years ago. Amazing professor, I really
need to check those videos again.

------
d41d8cd9
UC Berkeley vandalized their historical video lecture collection by deleting
it in response to a government ADA enquiry and pressure from "progressives" on
campus. Does anyone known why videos like those of Strang at MIT haven't had
the same fate?

------
riskneutral
This saved me in college

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zelphirkalt
The website is currently unreachable for me.

------
saystupidthings
For anyone using these videos now to help them learn linear algebra, id like
to suggest a FULL STOP and watch this YouTube playlist FIRST.

Strang is absolutely enlightening but I found it incredibly moreso after
watching 3blue1browns series on visualizing linear
algebra[https://www.youtube.com/playlist?list=PLZHQObOWTQDPD3MizzM2x...](https://www.youtube.com/playlist?list=PLZHQObOWTQDPD3MizzM2xVFitgF8hE_ab&app=desktop)

------
master_yoda_1
Cautionary note: you might better look for another resource to learn linear
algebra. Don’t waste your time watching these videos just because it is from
MIT

~~~
rfrey
Strang in general, and these videos in particular, are strongly recommended
every time self-teaching linear algebra comes up here. In 13 years on hacker
news I think this is the first negative thing about Strang I have read. Can
you expand on your criticism?

~~~
master_yoda_1
Strang course is too verbose and one does not need the whole course to do
practical work. Linear algebra done right is the book you need if you want to
apply in practice rather than just watching mit videos.
[https://www.amazon.com/Linear-Algebra-Right-Undergraduate-
Ma...](https://www.amazon.com/Linear-Algebra-Right-Undergraduate-
Mathematics/dp/3319307657/ref=asc_df_3319307657_nodl/?tag=hyprod-20&linkCode=df0&hvadid=312152840806&hvpos=&hvnetw=g&hvrand=4114625584809220351&hvpone=&hvptwo=&hvqmt=&hvdev=m&hvdvcmdl=&hvlocint=&hvlocphy=1014226&hvtargid=pla-684058077792&psc=1&tag=&ref=&adgrpid=61316181319&hvpone=&hvptwo=&hvadid=312152840806&hvpos=&hvnetw=g&hvrand=4114625584809220351&hvqmt=&hvdev=m&hvdvcmdl=&hvlocint=&hvlocphy=1014226&hvtargid=pla-684058077792)

------
momofarm
I wonder if all the teachers in MIT are as good as him?

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nu2ycombinator
How important is Linear Algebra for day to day work in FANG companies?

~~~
Myrmornis
Not. It's an extremely fundamental area of mathematics, necessary for really
understanding any mathematical subject (including statistics, machine
learning, signal processing etc) but it's not at all necessary for the vast
majority of programming / software engineering tasks, and indeed you'll find
excellent software engineers who haven't got a clue about linear algebra. I
think the reason you see it discussed on HN is because many people here are
interested in mathematics and that sort of theoretical way of thinking.

I don't mean to sound negative about it though. For example, the notions of
abstraction and interface are very important in both maths and software.

------
RSchaeffer
People frequently recommend Strang's teaching as an amazing pedagogical
approach for engineers and applied mathematicians, but I find I'm frustrated
every time I read his books or listen to his lectures. They don't work well
for me and I've found much better alternatives

~~~
Razengan
Sharing those alternatives would be a more valuable comment.

