Interactive Linear Algebra (2019)

Post by westurner » Fri, Aug 13, 2021, 7:38 PM UTC

screye wrote: post #31

For those interested in these kinds of interractive math experiences, I have been keeping track of them for a while. Here is my list so far: • https://www.intmath.com/ - Interactive Mathematics Learn math while you play with it • http://worrydream.com/LadderOfAbstraction/ - up and down the ladder of abstraction • https://betterexplained.com/ - Intuitive guides to various things in math • https://www.math3ma.com/blog/…

Post by ogogmad » Fri, Aug 13, 2021, 8:38 PM UTC

gugagore wrote: post #33

ogogmad wrote: post #26

Earlier quoted context omitted.

> 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…

> I actually had the latter one in mind: The one given by {A x | x^T x = 1}. I am near certain that you did not mean this. > When the semi-axes are parallel to the coordinate axes, the matrix is diagonal. Let D = the matrix | 2 0 | | 0 1 | And let R be any 2-by-2 rotation matrix. A = D * R would give you a locus of points (under {A x | x^T x = 1}) that has the semi-axes parallel to the coordinate axes. In general, A…

Post by gugagore » Fri, Aug 13, 2021, 9:18 PM UTC

ogogmad wrote: post #34

gugagore wrote: post #33

Earlier quoted context omitted.

> I actually had the latter one in mind: The one given by {A x | x^T x = 1}. I am near certain that you did not mean this. > When the semi-axes are parallel to the coordinate axes, the matrix is diagonal. Let D = the matrix | 2 0 | | 0 1 | And let R be any 2-by-2 rotation matrix. A = D * R would give you a locus of points (under {A x | x^T x = 1}) that has the semi-axes parallel to the coordinate axes. In general, A…

I only consider positive semi-definite symmetric matrices. A = D * R is almost certainly not such a matrix. The positive semi-definite symmetric case is the only one needed to compute SVDs. A proof of convergence for the algorithm is only known for certain families of matrices. These include the positive-definite symmetric matrices, all symmetric matrices (once suitable improvements to the algorithm are made), the He…

  A = Q^T * D * Q

Post by wirthjason » Sat, Aug 14, 2021, 1:01 AM UTC

chobytes wrote: post #9

scythmic_waves wrote: post #6

I'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 I prefer physical textbooks for many reasons I wont get in to... but I do really like the interactive and visualization elements computers offer. I feel like teaching kids some amount of coding to be able to play with math could be very helpful.

Post by ai_ia » Sat, Aug 14, 2021, 4:41 AM UTC

trees101 wrote: post #35

ai_ia wrote: post #20

Earlier quoted context omitted.

> 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…

Great work, thank you. Have you considered Obsidian, and Obsidian publish, as a medium? Take a look at Andy Matuschak's site as one example, there are many variants out there too https://notes.andymatuschak.org/About_these_notes