I 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 chain rule in calculus before drawing the geometric pictures of how derivatives are like slopes.
An illustrated introduction to linear algebra
11–20 of 91 posts
Re: An illustrated introduction to linear algebra
#12This is great. I really appreciate visual explanations and the way you build up the motivation. I'm using a few resources to learn linear algebra right now, including "The No Bullshit Guide to Linear Algebra", which has been pretty decent so far. Does anyone have other recommendations? I've found a lot of books to be too dense or academic for what I need. My goal is to develop a practical, working understanding I can…
>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 "cookbook" type resources but also not proof-heavy textbooks. Ideally something that builds intuition for the structures and operations that show up all over ML.
Re: An illustrated introduction to linear algebra
#13I 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.
Re: An illustrated introduction to linear algebra
#14Aditya Bhargava did it again. I have to say I am a fan already from the old days of Grokking Algorithms.
Thank you! I loved writing that book.
Re: An illustrated introduction to linear algebra
#15Did it end right when it says it will discuss the dot product?
Yep, that's going to be the next chapter!
Re: An illustrated introduction to linear algebra
#16Figures are blank on iOS Safari in dark mode.
Do you block images? Works for me on iOS Safari in dark mode. Every image also includes alt text (though I think the images add a lot).
Re: An illustrated introduction to linear algebra
#17That "Bam!" thing just brought Josh Starmer to mind. Anyone remember his book with the illustrated ML stuff? I used to watch his YouTube channel too. I really dig these kinds of explainers; they make learning so much more fun.
Re: An illustrated introduction to linear algebra
#18This is great. I really appreciate visual explanations and the way you build up the motivation. I'm using a few resources to learn linear algebra right now, including "The No Bullshit Guide to Linear Algebra", which has been pretty decent so far. Does anyone have other recommendations? I've found a lot of books to be too dense or academic for what I need. My goal is to develop a practical, working understanding I can…
> My goal is to develop a practical, working understanding I can apply directly
Same, and I think ML is a perfect use case for this. I also have a series for that coming.
Re: An illustrated introduction to linear algebra
#19I’m not even into math, but I enjoyed reading this very much. Kudos to the author!
Re: An illustrated introduction to linear algebra
#20A: this is cool, well done.
B: I miss scroll bars. I really, really miss scroll bars.