FYI, FB blocks this as "violating community standards" when you try to post it there.
And also, it's awesome!
Interactive Linear Algebra (2019)
21–30 of 43 posts
Re: Interactive Linear Algebra (2019)
#22I've only just skimmed through this. And it's a subject I already know so I can't tell if it's actually a good resource. However, my initial impression is that I love it. I think that textbooks, math textbooks in particular, are an example where print publishing does a disservice. (I'm counting PDFs here too.) By having to lay everything out in print form, you have to clutter up your explanations with examples and fo…
> I think that textbooks, math textbooks in particular, are an example where print publishing does a disservice. (I'm counting PDFs here too.) By having to lay everything out in print form, you have to clutter up your explanations with examples and footnotes that take up physical room. . I agree with your sentiment. Although, I believe there is bit of problem of generalizing it to a wider field. Surely, you can make…
I loved the comic. Have signed up. Will be looking forward your future courses.
Re: Interactive Linear Algebra (2019)
#23I've only just skimmed through this. And it's a subject I already know so I can't tell if it's actually a good resource. However, my initial impression is that I love it. I think that textbooks, math textbooks in particular, are an example where print publishing does a disservice. (I'm counting PDFs here too.) By having to lay everything out in print form, you have to clutter up your explanations with examples and fo…
> an example where print publishing does a disservice What would be an example (in the area of learning) where it does not? In the age of pervasive computing printed text is just that - a printout. A screenshot, if you will. Not extremely useful. Even a basic 3D model of something (like a car engine) that you could simply rotate and zoom is immensely more informative than a static picture of the same object. Text, su…
Professional color books (e.g. the Munsell soil books [1]) are a good example here. Screens use different, more restricted color spaces and are additive rather than subtractive.
I also have some books where the opposing page is used to hold the corresponding translation, so you can see both the original and its translation simultaneously. That breaks the page-at-a-time model of most document readers.
[1] https://www.amazon.com/Munsell-Soil-Book-Color-M50215B/dp/B0...
Re: Interactive Linear Algebra (2019)
#24This is great! This is a nice direction to go. Also, I don't mind if the creators would like to charge a small fee to use the book.
Re: Interactive Linear Algebra (2019)
#25It's confusing why ml beginners are obsessed over linear algebra. The subject is very hard and need only for advanced ml model. why not just study calculus and understand it?
Re: Interactive Linear Algebra (2019)
#26I wrote an entry on Wikipedia on visualizing the QR algorithm: https://en.wikipedia.org/wiki/QR_algorithm The visualization helped me spot an unstable fixed point and understand the behaviour of the algorithm near eigenvalue clashes. The behaviour's quite sophisticated. I think I wrote this there, but here goes again. The idea is that a positive-definite symmetric matrix can be visualized as an ellipse. This follows…
> a positive-definite symmetric matrix can be visualized as an ellipse. It is clear that you mean the ellipsoid as a set of points {x | x^T * A * x = 1} (or some other constant). There is another way in which all square matrices define an ellipsoid based on how the matrix transforms a unit sphere: {A*x | x^T * x = 1} (different matrices can map to the same ellipse here, however). I always like to clarify which one. (…
> It is clear that you mean the ellipsoid as a set of points {x | x^T * A * x = 1} (or some other constant). There is another way in which all square matrices define an ellipsoid based on how the matrix transforms a unit sphere: {A*x | x^T * x = 1} (different matrices can map to the same ellipse here, however).
I actually had the latter one in mind: The one given by {A*x | x^T * x = 1}. I hadn't thought of your other suggestion.
> (I unfortunately do not have intuition for the QR algorithm, but I am distracted by the description of an ellipse falling, as if it's rolling against the x-axis)
I don't know if this helps: https://ibb.co/DRDLzgJ
Each iteration causes it to rotate around the origin. The big semi-axis of the ellipse makes a smaller angle with the x-axis on each iteration. When the semi-axes are parallel to the coordinate axes, the matrix is diagonal.
Re: Interactive Linear Algebra (2019)
#27Being aware of the broad applications for Linear Algebra in engineering, I'm very eager to go through some Linear Algebra course on my own. But my problem is that I can't just learn from a text, even if it's interactive. I need to apply it to something. What are some fun projects that uses LA for an individual? I'm thinking about things like generative art, if anyone knows of any artists that inspire them.
You could try making a simple software-rendered 3D game from scratch. Basic 3D rendering is pretty much all linear algebra computations involving matrices and vectors.
Re: Interactive Linear Algebra (2019)
#28I hope that GATech one day offers an affordable online math MSc program, like their CS program
Re: Interactive Linear Algebra (2019)
#29Cool to see an article on the front page of HN from my alma mater :)
Re: Interactive Linear Algebra (2019)
#30Being aware of the broad applications for Linear Algebra in engineering, I'm very eager to go through some Linear Algebra course on my own. But my problem is that I can't just learn from a text, even if it's interactive. I need to apply it to something. What are some fun projects that uses LA for an individual? I'm thinking about things like generative art, if anyone knows of any artists that inspire them.
Check out “eigenfaces.” It’s straight forward and works reasonably well. There are a lot of interesting applications of PCA and SVD. Signal and noise separation, machine learning, the list goes on.