Appropriate use of the .xyz TLD :-)
Matrix Multiplication
21–30 of 135 posts
Re: Matrix Multiplication
#22This is a cool example of what Bret Victor calls an "Explorable Explanation" [0]. That said, I feel that it's more important to understand how and why matrix multiplication corresponds to a composition of linear transformations than learning the actual mechanics of doing the computation. You can get good at matrix multiplication without knowing what is going on. I view that as a less valuable activity than learning a…
Bingo. We did matrices in high school and even through a first linear algebra course in undergrad I got more or less competent at the mechanics of matrix multiplication without ever having any sense of why anyone would want to do this or why these rules, as opposed to some other set of rules that were equally formally valid, were of any interest. I could even tell you what the eigenvectors of a matrix were but had no sense of what that actually meant in terms of a linear transformation that matrix represented. Linear algebra is probably the area of math that is both universally important and completely skimped on by our education system.
Re: Matrix Multiplication
#23This is a cool example of what Bret Victor calls an "Explorable Explanation" [0]. That said, I feel that it's more important to understand how and why matrix multiplication corresponds to a composition of linear transformations than learning the actual mechanics of doing the computation. You can get good at matrix multiplication without knowing what is going on. I view that as a less valuable activity than learning a…
Bingo. We did matrices in high school and even through a first linear algebra course in undergrad I got more or less competent at the mechanics of matrix multiplication without ever having any sense of why anyone would want to do this or why these rules, as opposed to some other set of rules that were equally formally valid, were of any interest. I could even tell you what the eigenvectors of a matrix were but had no…
I feel very similar. Do you have any recommendations for resources to learn about why matrix multiplication is defined that way?
Re: Matrix Multiplication
#24Interesting, I wonder why Facebook has this website blocked, preventing me from posting it on my wall.
Re: Matrix Multiplication
#25This reminds me of Nicky Case's Explorable Explanation of a 2D transformation matrix: http://ncase.me/matrix/
Re: Matrix Multiplication
#26Earlier quoted context omitted.
Bingo. We did matrices in high school and even through a first linear algebra course in undergrad I got more or less competent at the mechanics of matrix multiplication without ever having any sense of why anyone would want to do this or why these rules, as opposed to some other set of rules that were equally formally valid, were of any interest. I could even tell you what the eigenvectors of a matrix were but had no…
I feel very similar. Do you have any recommendations for resources to learn about why matrix multiplication is defined that way?
Check out this series of videos "The Essence of Linear Algebra"[1] for a really powerful visual and intuitive explanation. It starts with vectors and builds to matrix multiplication and further to several other topics.
[1]: https://www.youtube.com/playlist?list=PLZHQObOWTQDPD3MizzM2x...
Re: Matrix Multiplication
#27This is a cool example of what Bret Victor calls an "Explorable Explanation" [0]. That said, I feel that it's more important to understand how and why matrix multiplication corresponds to a composition of linear transformations than learning the actual mechanics of doing the computation. You can get good at matrix multiplication without knowing what is going on. I view that as a less valuable activity than learning a…
In particular understanding that conjugation by another matrix is just a coordinate/frame transformation is crucial.
Relying to much on explicit coordinates many times obfuscates what's going on.
Re: Matrix Multiplication
#28Interesting, I wonder why Facebook has this website blocked, preventing me from posting it on my wall.
Good sign that it's time to leave Facebook. Really
Re: Matrix Multiplication
#29As others have mentioned, many introductions to linear algebra / matrix multiplication only gives the student a formula, but not why the formula looks like it does.
Why is matrix multiplication not pointwise, was something I had a hard time understanding.
Better explained has a good article on this, that really made it click for me
Re: Matrix Multiplication
#30As a gamedev who uses matrices all the time, I don't find this animation useful at all for practical work. Instead I think of matrix multiplication as creating a list of ordered operations (scale x translate x rotate etc) which is just encoded efficiently in a table, to then be sent to other parts of the program for use. You can even remove items from the list by multiplying by their inverse.