The idea is good but I am afraid it misses the point entirely. Multiplying both columns of the right hand side matrix to the left hand side matrix is really not helping the target audience understand what is going on. 2 operations are going on as the same time. I believe https://www.youtube.com/watch?v=XkY2DOUCWMU is a much better way to illustrate the matrix multiplication (and provide a clear explanation of the why) .
Matrix Multiplication
41–50 of 135 posts
Re: Matrix Multiplication
#42Earlier quoted context omitted.
I feel very similar. Do you have any recommendations for resources to learn about why matrix multiplication is defined that way?
"All the mathematics you missed but need to know for graduate school"[1] helped me a lot (and, in fact, I had and did). Once I had finished that, Cullen's "Matrices and linear transformations"[2] was really helpful too. But I wouldn't do Cullen if you're still, as I was, floundering with the concepts of why you're doing this in the first place. It's great once you have those concepts down. [1]: https://www.amazon.com…
Garrity's book looks exactly what I've been looking for for brushing up on basic math skills after a decade of fairly low-brow work after my MSc. Thanks for the reference!
Re: Matrix Multiplication
#43Uggg, why is zoom disable on mobile devices?
Re: Matrix Multiplication
#44This 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…
3Blue1Brown is an amazing youtube channel that provides very entertaining and educating visual explanation for all sorts of maths.
He has a whole series on linear algebra, including matrix mulitplication:
https://www.youtube.com/playlist?list=PLZHQObOWTQDPD3MizzM2x...
Re: Matrix Multiplication
#45This 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…
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Re: Matrix Multiplication
#46Earlier quoted context omitted.
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.
Is that true for non-square matrices?
Conjugation only makes sense for square matrices. More generally, left and right multiplication correspond to coordinate transformations of the output and input space, respectively.
Re: Matrix Multiplication
#47The idea is good but I am afraid it misses the point entirely. Multiplying both columns of the right hand side matrix to the left hand side matrix is really not helping the target audience understand what is going on. 2 operations are going on as the same time. I believe https://www.youtube.com/watch?v=XkY2DOUCWMU is a much better way to illustrate the matrix multiplication (and provide a clear explanation of the why…
Beat me to it :)
amazing channel!
Re: Matrix Multiplication
#48The idea is good but I am afraid it misses the point entirely. Multiplying both columns of the right hand side matrix to the left hand side matrix is really not helping the target audience understand what is going on. 2 operations are going on as the same time. I believe https://www.youtube.com/watch?v=XkY2DOUCWMU is a much better way to illustrate the matrix multiplication (and provide a clear explanation of the why…
Comments like these (aside from providing a nice link) just make authors of content sad. Why say such thing? You can say "here is another helpful link", but "misses the point entirely"? The point is to provide a self-evident mnemonic, as explained here: https://github.com/staltz/matrixmultiplication.xyz
Not nice.
Re: Matrix Multiplication
#49I like the idea, but my brain is wired differently. Usually, when I do matrix multiplications, the rows on the left side transition to the columns on the right side. In the example, the 1 goes to 2, 2 to 6, 1 to 1. The animation completely confused me, because it looks like being reversed, but the result is the same. Maybe, make this a visualization option?
There are several other visualizations that can be useful too:
Multiplication
We can see matrix by matrix multiplication from 5 different positions:
row by column multiplication
column at a time
row at a time
as sum of outer products
block multiplication
All of them are equivalent and lead to the same result
Does your mental model fit into one of these, or is it also reversed in the order it is applied? It would indeed be interesting to allow visualizations of all the approaches.
Re: Matrix Multiplication
#50Meh, the site is blocked at my workplace. Websense is really crummy.