For pure visual intuition, I prefer 3blue1brown's Essence of Linear Algebra on Youtube (https://www.youtube.com/playlist?list=PLZHQObOWTQDPD3MizzM2x...). 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.
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.
A thread from 2015 about that book: https://news.ycombinator.com/item?id=10183725.
I contacted one of the authors of the book. He confirms there aren't exercises yet, but says it's a work in progress and hopes there will be in the future.
Gilbert’s Linear Algebra course:
I’m rewriting fluid mechanics lecture notes in Jupyter (with Blender videos) and I’ve been looking for tools to visualise the maths. PyGel3D kinda works but it’s awkward and doesn’t work on nbviewer.
I’m 100% on board with the death of PowerPoint and my students seem to agree now that they’ve seen Jupyter.
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.
Looks like it's on pair with the Book of shaders.
(And a big +1 on the recommendation)
Another piece of technical documentation that stuck out to me recently as remarkably readable (though I haven't finished reading it): https://craftinginterpreters.com/
> Most engineering problems, no matter how complicated, can be reduced to linear algebra.
Most problems... except a problem of too much linear algebra.
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?
You might prefer Hefferon's Linear Algebra, also free and open-source, and which spends more time on this.
Both books look truly excellent.
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.
Thanks to representation theory, we can model vector spaces as R^n
Every finite dimensional vector space over the real numbers is isomorphic to R^n, for some n. But there is not always a canonical or "unique" isomorphism. I think the real difference -- and it is a subtle one -- is that R^n always comes with an "obvious" choice of basis, and many vector spaces don't.
I think the following may be the easiest interesting example. Consider the subspace of R^3, consisting of all (x, y, z) for which
x + y + z = 0.
This is a 2-dimensional real vector space. It is isomorphic to R^2, although in some sense it does not "present as such": you have to choose an isomorphism to R^2 if you want to "treat it as R^2", and there is no single choice that stands out.
In practice, one would not necessarily construct an isomorphism to R^2, or (more or less equivalently) exhibit a basis, before working with this vector space directly.
I'm not too familiar with representation theory. Do you know where I could find a worked example of constructing, say, a representation of (F_p)^m on R^n? (for prime p and m>1)
algebra: solving equations involving unknowns
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)