101–110 of 135 posts
Awesome. Some concepts in math are so much easier to grasp with an interactive visual. I once made an entire game around matrix multiplication -- such that players didn't even know they learned how to do this. And sometimes, visualizations can help cause discoveries. A lot of progress in theoretical physics came about because physicists 'guessed' what nature's equations should look like...and then got shocked when th…
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…
As part of the target audience (I didn't previously understand matrix multiplication, but now I do), you are definitely wrong. This does help the target audience understand what is going on. I think your core fallacy is that all people need to be taught in the same way, and that there is one correct way to teach people. The videos you link to may work for some people, but not for others. This explanation may work for…
This belief is why so many people are complaining about the site. Put simply I (and I assume others) do not believe that you understand matrix multiplication as a result of this site.
We could be wrong. Please explain matrix multiplication.
It's easier to think of matrix multiplication by computing the matrix elements, which means reducing the problem to NM vector dot products. To get the element of the result matrix at position (n,m), compute the inner product , where r_n is the nth row vector of the left matrix and c_m is the mth column vector of the right matrix. Once you try it, you'll see that it's also much easier to visualize than this strange, u…
Nope, won't ditch the domain. I'd recommend you ditch that type of speech.
Neat visualization. I feel it's important and eye-opening to note that there's not just one way to multiply matrices, there're five (according to Strang): 5 ways to multiply A B = C 1) Each element of C is a dot-product of corresponding rows of A with columns of B 2) Each column of C is a combination of the columns A. Each column of B has the coefficients. 3) Each row of C is a combination of the rows of B. Each row…
Earlier quoted context omitted.
This is why I'm a big fan of Axler's Linear Algebra Done Right . The book's emphasis is on the concepts behind the calculations rather than the calculations. I actually disagree with Axler on his avoidance of the determinant, though. I wish instead of avoiding it he'd spent more time developing it conceptually, as it's actually a fascinating construction. But to this day I have yet to find a gentler and better introd…
Axler's book is very good. An alternative to consider is Paul Halmos's much older Finite-Dimensional Vector Spaces [0]. Both books take the same basic approach, and the proofs of the major theorems are substantially the same. (Halmos's book is well known and well liked and was probably Axler's starting point.) Axler's book covers more ground (most notably, Halmos presents the polar decomposition but not the singular-…
Earlier quoted context omitted.
As part of the target audience (I didn't previously understand matrix multiplication, but now I do), you are definitely wrong. This does help the target audience understand what is going on. I think your core fallacy is that all people need to be taught in the same way, and that there is one correct way to teach people. The videos you link to may work for some people, but not for others. This explanation may work for…
>I didn't previously understand matrix multiplication, but now I do. This belief is why so many people are complaining about the site. Put simply I (and I assume others) do not believe that you understand matrix multiplication as a result of this site. We could be wrong. Please explain matrix multiplication.
I don't think that makes the site worthless or worthy of the some of the scorn I'm seeing in here.
I strongly agree with the complaint that "this completely misses the point" is super negative and dismissive and should be condemned.
If we-the-community want people to keep making things for fun or to try to help people, we have to criticize them graciously instead of saying that they are so wrong as to be useless. Not because it is moral or proper to do so, but because in practice dismissive and scornful negative feedback makes creators less likely to create new things or to try to improve old ones, and that's bad.
But that's just me.
This 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…