cat_man

4 ms·

1.
by cat_man 3y ago
You're right, I did mistakenly mix a few concepts together. The series representation for the function is infinite, like you say. What I was misapplying was the idea that a convergent infinite sum of matrix products (c0I + c1A + ... +
2.
by cat_man 3y ago
My memory is fuzzy on the details, but there's a way to show that if you have a series representation of a function that equals that converges to a=that function (i.e., an infinite sums of x^0, x^1, x^2, ..., x^n, ... with n going to i
3.
by cat_man 3y ago
Matrix functions (at least ones I learned about way back when) are Taylor series representations of a function with the matrix plugged in. For example: exp(A) = I + A + A^2/2 + ... + A^n/n! For matrices, you can show these end up
4.
by cat_man 4y ago
I've only watched about five of the videos on it, but Keenan Crane's intro to computer graphics series is pretty great (he's a CS professor at Carnegie Mellon): https://www.youtube.com/playlist?list=PL9_jI1bdZ
5.
by cat_man 4y ago
There are a couple of other comments that have mentioned oscillation modes, vibrations, etc. The first 7 pages of this series on sound synthesis might help give an idea of where these might come from: https://drive.google.com&#x2
6.
by cat_man 4y ago
> I got a B in Linear Algebra, and I still can't describe why you'd need that in the real world, while calculus/diff eq/discrete math were clearly tied to physics/thermodynamcis/computer science problems I k
7.
by cat_man 4y ago
I think it's a typo. \int_a^x f'(t)dt should be f(x) - f(a), and that would be the fundamental theorem of calculus (or some corollary of it). It looks like either f(a+x) should be f(x) or the upper limit x should be x+a. The rest