31–40 of 91 posts
Try actual problems that require you to use these tools and the inter-relationships between them, where it becomes blindingly obvious why they exist. Calculus is a prime example and it’s comical most students find Calculus hard because their LA is weak. But Calculus has extensive uses, just not for doing basic carb counting.
https://youtube.com/playlist?list=PLZHQObOWTQDPD3MizzM2xVFit...
Earlier quoted context omitted.
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
A: this is cool, well done. B: I miss scroll bars. I really, really miss scroll bars.
Earlier quoted context omitted.
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
I hadn't known about Learning from Data. Thank you for the link!
Earlier quoted context omitted.
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
Since you're associating ML with singular value decomposition, do you know if it is possible to factor the matrices of neural networks for fast inverse jacobian products? If this is possible, then optimizing through a neural network becomes roughly as cheap as doing half a dozen forward passes.
Less popular techniques like normalizing flows do need that but instead of SVD they directly design transformations that are easier to invert.
This is where the math nerds just can't help themselves, and I'm here for it. However, these things drive me crazy at the same time. You cannot have -4 nickels. In pure math with only x and y, sure those values can be negative. But when using real world examples using physical objects, no, you cannot have a negative nickel. Maybe you owe your mate the value of 4 nickels, but that's outside the scope of this lesson. Your negative nickels are not in another dimension (because again, the math works that way). You want to help people understand math with real world concepts but then go and confuse things with pure math concepts. And these negative nickels are still not even getting into imaginary nickels territory like you have square root of -4 nickels.
I feel like it's obligatory to also drop a link to the 3blue1brown series on linear algebra, for anyone interested in learning - it is a step up from what's in this post, but these videos are brilliant and still super accessible: https://youtube.com/playlist?list=PLZHQObOWTQDPD3MizzM2xVFit...