151–160 of 205 posts
Just curious .. what really are the usecases where of Linear Algebra is applied ? Any domain of software development ?
It's ridiculous how much random college-level linear algebra textbook material I stared at before things clicked in the course of just jumping in and exploring 3D graphics and writing my own 3D vector, matrix multiplication and 3D transform headers and using them in making some games in plain C. At some point it's like "Wait, is linear algebra really just about heaps of multiplication and addition? Like every dimensi…
Do you have any recommendations on videos/tutorials with graphics stuff that would help me grasp some of the linear algebra and basics about 2D/3D graphics? Your comment about 'staring at random college-level linear algebra' stuff resonated deeply with me, and I've always felt like I'm just not understanding how it all connects.
If you've never written a standalone software-rendered ray tracer, I found that to be a very useful exercise early on. There are plenty of tutorials for those on the interwebs.
I'm currently trying to grok the finite element method. Gilbert Strang's explanation of the transition from the Galerkin method to FEM did more for me in terms of connecting the dots than anything else I could find on the web. And it wasn't even a lecture, just a kind of an interview. I think it's this one: youtube.com/watch?v=WwgrAH-IMOk
https://www.youtube.com/watch?v=WwgrAH-IMOk I feel like I don't really understand his explanation, because it's kind of vague. But I think that might be because you've seen the equations dozens of times, and I haven't seen them at all, so you were prepared to understand the video.
Earlier quoted context omitted.
"A monad is just a monoid in the category of endofunctors, what's the problem?"
I don't think this definition is correct. (A monad is an endofunctor.)
The claim is that in other categories, there might be other natural combinations between two objects, for example a tensor product of Abelian groups combined with the integers Z as unit, or a composition of two endofunctors into a new endofunctor F ∘ F combined with the identity functor.
So the idea is that a monoid is somehow a destroyer of this combination operation; a monoid in sets un-combines the Cartesian product M × M back into the set M, and indeed this is a function (a set-arrow) from the combined objects to the underlying object.
By having an endofunctor combined with a natural transformation from F ∘ F back to F (natural transformations are the arrows in the category of endofunctors) a monad is therefore doing exactly what a monoid does, if you replace the "pre-monoid" combination step of the Cartesian product with instead a new "pre-monoid" combination step of endofunctor composition.
Earlier quoted context omitted.
https://www.youtube.com/watch?v=WwgrAH-IMOk I feel like I don't really understand his explanation, because it's kind of vague. But I think that might be because you've seen the equations dozens of times, and I haven't seen them at all, so you were prepared to understand the video.
This makes sense. As said, it was about connecting the dots for me. Also, I don't even claim I fully understand FEM (or even Galerkin), it's just my hobby project.
I had very intelligent linear algebra professor in college but he was, in my opinion, a very poor communicator. I paid attention to lectures and stared at the text, but couldn't really understand the material. For the first part of a linear algebra course, students who don't mind blindly following mechanical processes for solving problems can do very well. Unfortunately I'm one of those people who tends to reject the…
> I paid attention to lectures and stared at the text, but couldn't really understand the material. For the first part of a linear algebra course, students who don't mind blindly following mechanical processes for solving problems can do very well. I had a similar, though sort of opposite experience. In high school, I breezed through the material, and started teaching myself calculus during the summer to prepare for…
Some of the concepts made sense, especially solving for linear systems of equations.
Recently, I decided to brush up on my math skills via Youtube videos, and came across this series: https://www.youtube.com/channel/UCYO_jab_esuFRV4b17AJtAw
It explains Linear Algebra concepts using 2D and 3D vector manipulation, and the animations help me visualize the underlying maths.
After watching this and having read the comments, I am quite puzzled by the approach American seem to take to linear algebra. Are matrices viewed as the core of the subject in the USA ? My country curriculum introduces linear algebra through group theory and vector spaces. Matrices come later.
There's nothing particularly linear about groups.
Earlier quoted context omitted.
This makes sense. As said, it was about connecting the dots for me. Also, I don't even claim I fully understand FEM (or even Galerkin), it's just my hobby project.
That sounds interesting! What are you doing with it?
Maybe I will create a game prototype based on the mechanics but this is just a vague idea.
After watching this and having read the comments, I am quite puzzled by the approach American seem to take to linear algebra. Are matrices viewed as the core of the subject in the USA ? My country curriculum introduces linear algebra through group theory and vector spaces. Matrices come later.
It's not universal.