
Interactive Linear Algebra - kondor
https://textbooks.math.gatech.edu/ila/
======
bhntr3
So far I think I prefer the visualizations in
[http://immersivemath.com/ila/index.html](http://immersivemath.com/ila/index.html)

For pure visual intuition, I prefer 3blue1brown's Essence of Linear Algebra on
Youtube
([https://www.youtube.com/playlist?list=PLZHQObOWTQDPD3MizzM2x...](https://www.youtube.com/playlist?list=PLZHQObOWTQDPD3MizzM2xVFitgF8hE_ab)).
Even though they're not interactive, the visualizations themselves are the
most compelling and insightful.

Has anyone used both interactive texts? My initial impression is that the GA
Tech text starts with matrices and applications to systems of equations (like
Strang) while the immersive math one seems to start more focused on vectors
and geometry with computer graphics applications.

Neither seems to have supporting exercises yet which I think really limits
their use as primary texts.

~~~
sh-run
I took linear algebra after college (I hold a non-technical bachelors) through
a local community college.

3blue1brown is what made linear algebra really click for me. My professor also
gave us some jupyter notebooks to play around with that really helped.
Unfortunately he developed these himself and I don't believe they are publicly
accessible.

I also purchased 'Coding the Matrix' by Philip N. Klein, which gave me another
perspective on Linear Algebra. I primarily used it as an additional reference.
I've been meaning to do a front to back reading of the text, but haven't
gotten around to it yet. It's got some pretty decent exercises.

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melling
Lex Friedman interviews Gilbert Strang this week:

[https://youtu.be/lEZPfmGCEk0](https://youtu.be/lEZPfmGCEk0)

Gilbert’s Linear Algebra course:

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

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thinkingkong
This is based on Mathbox which is... brilliant. Here's the demo blog post that
shows off what it can do:
[https://acko.net/blog/mathbox2/](https://acko.net/blog/mathbox2/)

~~~
syntaxing
I normally skim through these types of articles but the visualization that
s/he demos is so captivating and hypnotizing

~~~
romwell
Acko is Steven Wittens[1]; no need to use a pronoun when we have a name :)

[1][https://acko.net/about](https://acko.net/about)

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impendia
This looks outstanding.

I am a math professor, and I need to choose a book next time I teach linear
algebra. It may well be this one.

If anyone has in-depth experience with the book, I'd be grateful to hear about
it.

~~~
qqaazz
It covers most of the standard material in an introductory Linear Algebra
course. There is one large omission: the textbook completely ignores the
notion of change of basis. There is no explanation why this was done, and a
guess is that it was overlooked. The book is also very streamlined, and does
not have much outside of the standard curriculum (which might be a plus).

~~~
cbolton
Change of basis is covered in section 5.3 on "similarity". See in particular
the subsection "Geometry of Similar Matrices".

~~~
qqaazz
Aha. It appears it was just skipped in the curriculum rather,
[http://people.math.gatech.edu/~cjankowski3/19f/m1553/webpage...](http://people.math.gatech.edu/~cjankowski3/19f/m1553/webpage/2019f-schedule.html).

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tiborsaas
I love how approachable the writing style is. It's very easy to write a
technical introduction that assumes a lot of pre-existing knowledge of the
reader. So far it's a great read for someone like me who got discouraged by
notation and cloudy terms before.

Looks like it's on pair with the Book of shaders.

~~~
newnewpdro
The Book of Shaders is half vaporware, or am I missing something?

~~~
percentcer
yeah seems like they never finished it :( first half is great though

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iLemming
Also great resource: [https://aiprobook.com/numerical-linear-algebra-for-
programme...](https://aiprobook.com/numerical-linear-algebra-for-programmers)

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Zhyl
Reminds me of the Nicki Case tool:

[https://ncase.me/matrix/](https://ncase.me/matrix/)

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majke
From
[https://textbooks.math.gatech.edu/ila/overview.html](https://textbooks.math.gatech.edu/ila/overview.html)

> Most engineering problems, no matter how complicated, can be reduced to
> linear algebra.

Most problems... except a problem of too much linear algebra.

~~~
black6
Everything is linear when plotted log-log with a fat magic marker.

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kd0amg
_Linear: having to do with lines, planes, etc._

This definition makes me worry that the book is going to operate entirely in
R^n. Is there anything here about substantively different vector spaces?

~~~
sitkack
Is it a real concern or are you humble bragging about the lack of advanced
math in an introductory text on _linear_ algebra?

~~~
throwawaymath
No, that's a legitimate concern. It may or may not be relevant for what you
specifically care about, but it's definitely a legitimate thing to ask about.

It's not uncommon for even undergraduate linear algebra to cover abstract
spaces and notions of linearity which generalize beyond _R^n_. For example,
the function space _P_n_ consisting of all polynomials with degree less than
or equal to _n_. Hoffman-Kunze, Halmos, Axler and Friedberg-Insel-Spence are
all examples of undergraduate textbooks which cover this material.

This isn't just theoretical. Function spaces like _P_n_ are useful in applied
mathematics. And even if you don't use function spaces, it's very common for
engineers, physicists and applied mathematicians to work in the complex space
_C^n_ rather than _R^n_.

~~~
vcxy
This is just the first semester course. In my experience teaching it at GT, it
is mostly taken by freshman, and I'm not sure how many majors require it but
my students have come from a huge variety of majors. I'm not sure that
abstract vector spaces is that useful for, say, psychology majors. There is a
second semester course that usually uses Axler.

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jacobsimon
Wonderful! I remember struggling to make it through linear algebra in college
because the teaching style was so unapproachable and disconnected from real
applications. It wasn't until I took computer graphics that I really grasped a
lot of the concepts.

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Aardwolf
Good stuff.

One point of feedback: when making a widget fullscreen and then pressing the
back button, you're back at the previous chapter, rather than scrolled at the
position you left in the current chapter.

I see now there's also a "make small again" button far down in the bottom
right, but it's still a trap.

Probably it's solved either by having the back button close the widget, or
alternatively make the widget look more like an overlay and less like a new
page (plus closing with "esc" would also help)

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krosaen
This is really neat, and it's clear a lot of work went into the polish and
interactivity. I'd love to see the elimination examples extended to show how
LU factorization falls out of those steps. It seems like a key thing to grasp
and lays the groundwork for understanding of related matrix factorizations
like symmetric, QR and singular value decomposition.

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photon_lines
If anyone is interested in a similar intuitive or geometric guide I open
sourced my own notes and you can find them here:
[https://github.com/photonlines/Intuitive-Overview-of-
Linear-...](https://github.com/photonlines/Intuitive-Overview-of-Linear-
Algebra-Fundamentals)

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gautamcgoel
I had one of the authors (Dan Margalit) as a prof when I was a math undergrad
at Georgia Tech. Cool guy and a great instructor.

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mamazaco
This is our (my company) take on Linear Algebra, but then with exercises:

[https://app.bolster.academy/courses/chapters/en/6](https://app.bolster.academy/courses/chapters/en/6)

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lotaezenwa
This extensively uses the American Institute of Math's knowls[0], which I
think is excellent for math documentation.

[0] [https://aimath.org/knowlepedia/](https://aimath.org/knowlepedia/)

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kernoble
Awesome for reference and understanding. Anyone know of good practice
material? Or maybe thinking of a way of generating practice material that
exercises the component skills needed to do/understand Linear Algebra?

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perl4ever
I got an A- in linear algebra in college without learning _anything_ , via
multiple choice tests and pattern recognition. Recently, it's started to seem
like a metaphor for the state of AI.

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s3arch
Is there anything like this for other areas in mathematics such as Number
Theory?

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Jahak
Good job. Thank you very much.

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x7k
Thank you

