
Linear Algebra Done Right Video Series - seycombi
https://www.youtube.com/channel/UCtHp0WNe3OaSXAr1C_Oi0AQ/videos
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kharms
This playlist gives a very nice geometric intuition to a lot of the
foundational concepts of linear algebra:

[https://m.youtube.com/playlist?list=PLZHQObOWTQDPD3MizzM2xVF...](https://m.youtube.com/playlist?list=PLZHQObOWTQDPD3MizzM2xVFitgF8hE_ab)

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badosu
All videos from 3blue1brown are amazing! Followed up through the latest
'Essence of Calculus' series, really a gem.

He makes the software used to create the animations and it's open-source:
[https://github.com/3b1b/manim](https://github.com/3b1b/manim)

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gajjanag
Really good stuff from what I could tell from a glance at this! "Linear
Algebra Done Right" is a terrific book, though personally I favor Lax's book:
"Linear Algebra and its Applications". I have not studied Terence Tao's notes
(which I obtained from AMS's link for "open math notes")
[https://www.ams.org/open-math-notes/omn-view-
listing?listing...](https://www.ams.org/open-math-notes/omn-view-
listing?listingId=110650). Based on what I know of Tao's writing in general,
this should be fun.

Note that these references have a more "abstract" viewpoint (e.g focusing on
"coordinate-free" methods, such as linear operators as opposed to matries as
the fundamental object) than that advocated and taught by Strang. I do not
know in the end which is better for an absolute beginner. All I can guarantee
is that the abstract viewpoint is definitely needed and far more useful for
anyone using math beyond its basics. This includes (but is not limited to)
machine learning and optimization.

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woopwoop
I haven't read Lax's linear algebra book, but I fell in love with his
functional analysis book in the summer before I began grad school. His notes
on hyperbolic pde are also great. Lax is of course a great mathematician, but
he is also an incredibly lucid writer. He doesn't make anything more difficult
than it needs to be. I would recommend reading anything written by him that
you can get your hands on.

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gajjanag
Thanks a lot for this endorsement of his functional analysis book. I never got
around to understanding functional analysis properly; mainly because I don't
work on PDE's/control theory that would have used the ideas more heavily.
Added to my todo list.

Not really on topic, but I would like to use this opportunity to express
gratitude to the HN community - although this forum is mostly tech-centric, it
is wonderful to see things like this post get interest and discussion.

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tanderson92
Thank you for saying so! It's good to not feel left out. There are plenty of
mathematicians and applied mathematicians here, too. We just do not comment on
the JS/Rust discussions :)

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valesco
I gathered the videos into a playlist for better findability:
[https://www.youtube.com/playlist?list=PLF9bYy39t4tGBnJ9FjOSF...](https://www.youtube.com/playlist?list=PLF9bYy39t4tGBnJ9FjOSFpb6IVchMh5Sv)

~~~
liamondrop
Thanks for that!

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amelius
I like this series by Gilbert Strang:

[https://ocw.mit.edu/courses/mathematics/18-06-linear-
algebra...](https://ocw.mit.edu/courses/mathematics/18-06-linear-algebra-
spring-2010/video-lectures/)

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fellellor
I was recently trying to understand wireless channel estimation. So supposedly
at the reciever we have to pass the signal through, an inverse channel filter
to recover the transmitted signal. A friend of mine asked: what if the channel
has no inverse? I had no idea how to respond to this because of my poor
intuitive understanding of linear algebra.

3blue1brown's video series explained this beautifully as, when the inverse
doesn't exist, the transformation packs the input into a lower dimensional
space. So in communication terms the transmitted signal is completely lost
anyway. So we should look for a better channel to communicate.

Now needless to say there is a lot I am probably wrong about, but I'm still
very grateful for that excellent video series.

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ianai
As a rogue mathematician I miss linear algebra.

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master_yoda_1
I really think Gilbert Strang's lectures are responsible for creating the
impression that linear algebra is hard. I watched that lecture and it was all
dry math and very few intuitions. "Linear algebra done right" is a better
book. Come on we are in 21st century and our intelligence has evolved so that
we can understand the 16th century math better :)

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smithsmith
We have limited attention span in 21st century. The teaching content better be
interesting with low cognitive load required to understand using animations to
get the material in to the brain. This is the right direction.

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geokon
If you want a more advanced book I really strongly recommend Matrix Analysis
and it's Applications by Carl Meyer. Very clear and concise and the problems
are well written. It's my all time favorite math book. But this is really if
you want to absorb a lot of more-advanced linear algebra with a lot less fluff
and exposition than Strang

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data_scientist
Does anyone have a good book for advanced linear algebra? I learned the basics
in school - eg. Matrix diagonalization, svd) but I need for ml to really
understand things like angle between flats, tensor decomposition, etc

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perseusprime11
It will be nice if somebody ever does a version of (I) here's the theory
behind a linear algebra equation, and then, (ii) here's a real world
application.

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romwell
First, math (linear algebra in particular) is not at all about equations. The
format you said is very limiting, because most of the important things in
linear algebra are not equations: vector spaces, basis, norms, orthogonality,
diagonalization, eigenvalues, etc.

Second, if you crave for applications, check out this free linear algebra
book: Linear Algebra Done Wrong by Serge Treil
([https://www.math.brown.edu/~treil/papers/LADW/LADW.html](https://www.math.brown.edu/~treil/papers/LADW/LADW.html))

His book has a lot of applications, and has been written as a response to
Axler's book, which does not (even though I think that Axler's way is the
best).

Finally, No Bullshit Guide to Linear Algebra tries to do _exactly_ what you
want: the presentation aims to be

(I)here's a concept (II)here's a real-world application

The book is here:
[https://gumroad.com/l/noBSLA](https://gumroad.com/l/noBSLA), $29

(I found out about this book on Hackernews, which seems to be a pretty decent
place for such things)

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perseusprime11
Thanks for he links. I'll check them out. No Bullshit guide seems interesting.

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curiousgal
In my expereince, nothing beats practice.

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geezerjay
If you want to play the game, first you need to learn the rules.

Theory beats practice, because without theory there is no practice.

