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Fundamentals of Linear Algebra and Optimization [pdf]

seas.upenn.edu

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Re: Fundamentals of Linear Algebra and Optimization [pdf]

#11

Post by edanm »

zengid wrote: post #4
alexcnwy wrote: post #2

This is great! There's so much hype about machine learning but so few people seem to appreciate the fundamental importance of linear algebra (especially in ML). This fast.ai course is also great: http://www.fast.ai/2017/07/17/num-lin-alg/

Cool new course! I'm thinking about taking their Practical Deep Learing for Coders course at the moment: http://course.fast.ai/

If you're at all interested in actually doing deep learning, then do the course! It's by far my favorite resource for actually learning to do deep learning.

Of course it won't give you the math background, but you can abd should pick it up after.

Re: Fundamentals of Linear Algebra and Optimization [pdf]

#12

Post by mpowell94 »

mindcrime wrote: post #5
glbrew wrote: post #3

Is this going to be a textbook? I can't find it in print, but it looks like a great text.

Good question. I'm honestly not sure. I just stumbled across it while looking for linalg resources. It appears to be legit, since the author is with UPenn and it's on a upenn.edu site. But I don't see an explicit license notification or anything, so not sure if you're even allowed to print it out yourself or not.

Was in his class at Penn, he gives all this stuff away with no issue. Didnt have to pay anything for course materials and its all open to the public.

Re: Fundamentals of Linear Algebra and Optimization [pdf]

#13

Post by hvs »

I may be a troglodyte, but I was bored senseless in my linear algebra, calculus, discrete mathematics, statistics, etc classes in college. Then they tag all the interesting stuff like AI (we didn't call it Machine Learning back in the 90s) at the end of your major where you actually use it. I had to go back and relearn it all because I didn't pay attention the first time. Note to mathematicians (or at least math professors): lead with the interesting stuff before the theory. It'll make learning easier and more fun.

Re: Fundamentals of Linear Algebra and Optimization [pdf]

#15

Post by SonOfLilit »

My test for linear algebra books is how they first present matrices and matrix multiplication.

If they define a matrix as an NxM table of numbers with a multiplication operation defined as this complicated formula with a couple of nested sigmas, and then much later a lemma is mentioned that says every linear transformation can be represented as a matrix and then the composition of two transforms is the matrix multiplication of their matrix forms, I throw the book away in disgust. I throw most books away in disgust.

This is the second book I've seen that does it right, but unlike the other one [1] this one wraps the very correct presentation of matrices in so much technical language and such a boring cover story that I almost threw it away in disgust anyway.

My greatest wish in STEM education is that we teach linear algebra better. It's such low hanging fruit and could change so much!

[1] which I saw linked in HN a year ago and don't remember the name of, but it was something like "linear algebra taught the correct way" and was apparently well known in the States so ask your friends

Re: Fundamentals of Linear Algebra and Optimization [pdf]

#16

Post by jpau »

SonOfLilit wrote: post #15

My test for linear algebra books is how they first present matrices and matrix multiplication. If they define a matrix as an NxM table of numbers with a multiplication operation defined as this complicated formula with a couple of nested sigmas, and then much later a lemma is mentioned that says every linear transformation can be represented as a matrix and then the composition of two transforms is the matrix multipl…

Might [1] be "Linear Algebra Done Right" by Axler? http://www.springer.com/gp/book/9783319110790

Re: Fundamentals of Linear Algebra and Optimization [pdf]

#17

Post by Eridrus »

hvs wrote: post #13

I may be a troglodyte, but I was bored senseless in my linear algebra, calculus, discrete mathematics, statistics, etc classes in college. Then they tag all the interesting stuff like AI (we didn't call it Machine Learning back in the 90s) at the end of your major where you actually use it. I had to go back and relearn it all because I didn't pay attention the first time. Note to mathematicians (or at least math prof…

I'm basically in the same boat, except I thought our AI class was basically just A* and other forms of search and didn't go back to learning any of it until after university!

Re: Fundamentals of Linear Algebra and Optimization [pdf]

#18

Post by andars »

SonOfLilit wrote: post #15

My test for linear algebra books is how they first present matrices and matrix multiplication. If they define a matrix as an NxM table of numbers with a multiplication operation defined as this complicated formula with a couple of nested sigmas, and then much later a lemma is mentioned that says every linear transformation can be represented as a matrix and then the composition of two transforms is the matrix multipl…

The Friedberg, Insel, Spence book [1] passes your test. Linear transformations first, then matrices as a representation of transformations with respect to a specified basis. Depending on your tastes, you may find it too dry, but imo it is a clean presentation.

[1]: https://www.amazon.com/Linear-Algebra-4th-Stephen-Friedberg/...

Re: Fundamentals of Linear Algebra and Optimization [pdf]

#19

Post by abecedarius »

SonOfLilit wrote: post #15

My test for linear algebra books is how they first present matrices and matrix multiplication. If they define a matrix as an NxM table of numbers with a multiplication operation defined as this complicated formula with a couple of nested sigmas, and then much later a lemma is mentioned that says every linear transformation can be represented as a matrix and then the composition of two transforms is the matrix multipl…

Another text that starts with linear transformations is Apostol’s Calculus. It’s somewhat more concrete than Axler, IIRC — e.g. it doesn’t try to avoid determinants, but starts with properties of volume-scaling and then develops the determinant formula out of those. We used this text for freshman/sophomore math back in the 80s, so my memory is fuzzy; but I liked it a lot.

Re: Fundamentals of Linear Algebra and Optimization [pdf]

#20

Post by begriffs »

SonOfLilit wrote: post #15

My test for linear algebra books is how they first present matrices and matrix multiplication. If they define a matrix as an NxM table of numbers with a multiplication operation defined as this complicated formula with a couple of nested sigmas, and then much later a lemma is mentioned that says every linear transformation can be represented as a matrix and then the composition of two transforms is the matrix multipl…

I think the book you're talking about is Axler's "Linear Algebra Done Right." I worked through the problems in this book with some friends, and it is a very good presentation.

After doing that book I wanted to see what other books were out there, which ones were the good ones, and sort of classify them. I came up with this list: https://begriffs.com/posts/2016-07-24-best-linear-algebra-bo...

I classify the books as Generalist (like Axler's), Theoretical (starting from e.g. modules rather than vector spaces), Numerical (matrix normal forms and algorithms), Practice (books full of problems), and a few other categories.

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