Did it end right when it says it will discuss the dot product?
Yep, that's going to be the next chapter!
Ok, please add that sentence because I spent two minutes looking everywhere for the next paragraph.
An illustrated introduction to linear algebra
21–30 of 91 posts
Re: An illustrated introduction to linear algebra
#22A: this is cool, well done. B: I miss scroll bars. I really, really miss scroll bars.
I see a scroll bar in Firefox and in Chrome...
Re: An illustrated introduction to linear algebra
#23I really like this, and I think one way to make it even more clear would be to use other variable letters to represent breads and milks, because their x’s and y’s somehow morph into the x’s and y’s that represent carbs and protein in the graph.
Re: An illustrated introduction to linear algebra
#24I really like the second part of the blogpost but starting with Gaussian elimination is a little "mysterious" for lack of a better word. It seems more logical to start with a problem ("how to solve linear equations?" "how to find intersections of lines?"), show its solution graphically, and then present the computational method or algorithm that provides this solution. Doing it backwards is a little like teaching the…
Author here – I think you're probably right. I wrote the Gaussian elimination section more as a recap, because I figured most readers have seen Gaussian elimination before, and I was keen to get to the rest of it. I'd love to hear if other folks had trouble with this section. Maybe I need to slow it down and explain it better.
Loved the article, and also the shoutout to Strang's lectures.
I agree with the order, the Gaussian should come later I almost closed the article - glad I kept scrolling out of curiosity.
Also I felt like I had been primed to think about nickles and pennies as variables rather than coefficients due to the color scheme, so when I got to the food section I naturally expected to see the column picture first.
When I encountered the carb/protein matrix instead, I perceived it in the form:
[A][x], where the x is [milk bread].T
so I naturally perceived the matrix as a transformation and saw the food items as variables about to be "passed through" the matrix.
But another part of my brain immediately recognized the matrix as a dataset of feature vectors, [[milk].T [bread].T], yearning for y = f(W @ x).
I was never able to resolve this tension in my mind...
Re: An illustrated introduction to linear algebra
#25As much as I like posts like this I can't feel anything other than hate for the substack platform, it just sucks I'm sorry but I can't understand how people can rely on that bloated web app. I just click around and it's so slow and buggy, recently I canceled a subscription because it kepts signin me out and the signup signin experience just suck
Re: An illustrated introduction to linear algebra
#26Earlier quoted context omitted.
>My goal is to develop a practical, working understanding I can apply directly. Apply directly... to what? IMO it is weird to learn theory (like linear algebra) expressly for practical reasons: surely one could just pick up a book on those practical applications and learn the theory along the way? And if in this process, you end up really needing the theory then certainly there is no substitute for learning the theor…
You're totally right. I left out the important context. I'm learning linear algebra mainly for applied use in ML/AI. I don't want to skip the theory entirely, but I've found that approaching it from the perspective of how it's actually used in models (embeddings, transformations, optimization, etc.) helps me with motivation and retaining. So I'm looking for resources that bridge the gap, not purely computational "coo…
Strang's Linear algebra and learning from data is extremely practical and focused on ML
https://math.mit.edu/~gs/learningfromdata/
Although if your goal is to learn ML you should probably focus on that first and foremost, then after a while you will see which concepts from linear algebra keep appearing (for example, singular value decomposition, positive definite matrices, etc) and work your way back from there
Re: An illustrated introduction to linear algebra
#27Seems a bit premature? This is "linear algebra" in the sense of middle/high school algebra in linear equations. I suppose many more chapters are coming?
Re: An illustrated introduction to linear algebra
#28I really wish I had math taught to me like this at school. I feel like my life would have gone in a very different direction!
Re: An illustrated introduction to linear algebra
#29This is nice. Until I took an actual semester of it in college, linear algebra was a total mystery to me. Great job.
For those unfamiliar with vectors, it might be helpful to briefly explain how the two vectors (their magnitude and direction) represent the one bread and one milk and how vectors can be moved around and added to each other.
Re: An illustrated introduction to linear algebra
#30this was my least favorite math subject in college, probably one of the most difficult class I took.