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Introduction to Linear Algebra for Applied Machine Learning with Python

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Re: Introduction to Linear Algebra for Applied Machine Learning with Python

#31

Post by egsmi »

BossingAround wrote: post #25

I just recently finally bought Strang's introduction to Linear Algebra. The book itself is very dense and, dare I say, scary to a newcomer, but his videos are amazingly clear in combination with the book. I am in the beginning, but so far, I'd recommend the book. Though, the steep price (almost 100USD over here) makes it a bit difficult to recommend. I might buy Boyd’s and Vandenberghe’s Introduction to Applied Linea…

Jim Hefferon, who is also a HN member, has a great free Linear Algebra textbook. People all have their own preferences but I actually prefer his to Strang's.

https://hefferon.net/linearalgebra/

Re: Introduction to Linear Algebra for Applied Machine Learning with Python

#32

Post by gspr »

joshvm wrote: post #21
tomcat27 wrote: post #4

are there resources where linear algebra is discussed in the context of deep learning?

Accompanying the book in the sibling comment is Strang's MIT 18.065 course which is exactly what you're after (it specifically covers linear algebra with a focus on data science and ML): https://ocw.mit.edu/courses/mathematics/18-065-matrix-method... OCW so it's free(!), including the videos and handouts.

And Strang (more than) knows what he's talking about. Unlike OP, who treats minor corrections as personal attacks and goes all defensive. This is part of the reasons why it's dangerous to replace education from established institutions with random blogs on the internet.

Re: Introduction to Linear Algebra for Applied Machine Learning with Python

#33

Post by Tainnor »

redvenom wrote: post #26
gspr wrote: post #20

I was scrolling through to see if you explain how you typeset the math (notoriously hard on webpages), but I happened to instead find a small mistake. You write: "Elements of $\mathbb{R}^n$ are sets of real numbers." That is an incorrect definition. - It is inaccurate because n doesn't enter into the definition (and thus all Euclidean spaces would be the same). - You want ordered n-tuples, not sets. If you actually d…

Totally agree with this post...however, to be extremely pedantic (and thus not suitable for the article in question), a tuple in the foundations of mathematics is typically defined as a set. That is, (x,y) := {x,{x,y}}, where the latter is the set containing the element x and the set {x,y}. That is how one goes from axiomatic set theory to define tuples of numbers.

To be even more pointlessly pedantic: sure, but that doesn't give you "sets of real numbers", in the sense of sets where every element can meaningfully be interpreted as a real number.

Re: Introduction to Linear Algebra for Applied Machine Learning with Python

#34

Post by giu »

egsmi wrote: post #31
BossingAround wrote: post #25

I just recently finally bought Strang's introduction to Linear Algebra. The book itself is very dense and, dare I say, scary to a newcomer, but his videos are amazingly clear in combination with the book. I am in the beginning, but so far, I'd recommend the book. Though, the steep price (almost 100USD over here) makes it a bit difficult to recommend. I might buy Boyd’s and Vandenberghe’s Introduction to Applied Linea…

Jim Hefferon, who is also a HN member, has a great free Linear Algebra textbook. People all have their own preferences but I actually prefer his to Strang's. https://hefferon.net/linearalgebra/

+1 for Heffron's book, which was posted here 2 weeks ago [0]. He also published all the solutions to the exercises! [1]

[0] https://news.ycombinator.com/item?id=24892907

[1] http://joshua.smcvt.edu/linearalgebra/jhanswer.pdf

Re: Introduction to Linear Algebra for Applied Machine Learning with Python

#36

Post by Tainnor »

Konohamaru wrote: post #27

It's not on the syllabus, but what application does jordan canonical form have to machine learning?

probably none, since afaik the Jordan normal form is numerically very unstable. It's however quite useful in proofs (e.g. you can theoretically construct the matrix exponential out of it).

Re: Introduction to Linear Algebra for Applied Machine Learning with Python

#38

Post by PNWChris »

init-as wrote: post #6

Is there a website that anyone knows of for these types of open-source curriculums? Feel like it would be nice to have a place where people could post these and you could reference them when you wanted to learn something in the correct order and with the best resources.

They’re much narrower in scope than a full curriculum (or even a course, for that matter), but Better Explained [0] has some very good overviews of math topics. They are a useful supplement I’ve come across repeatedly while searching topics I found challenging over the years.

On the topic of open source learning, I take every chance I can to heartily recommend fast.ai’s course [1]. It’s a good intro to Deep Learning that leaves you informed enough to build things, and equips you to ask follow-on questions and dive deeper when/where you need to.

[0]: https://betterexplained.com/

[1]: https://course.fast.ai/

Re: Introduction to Linear Algebra for Applied Machine Learning with Python

#39

Post by aanet »

This looks like an excellent resource. Thank you.

The rendering of some of the Latex code does seem to be bit of a challenge; I see some intermingled code/text (on latest Mozilla on Ubuntu 18). The CPU usage also shoots up.

What scripts are rendering the Latex code?

Re: Introduction to Linear Algebra for Applied Machine Learning with Python

#40

Post by jph00 »

PNWChris wrote: post #38
init-as wrote: post #6

Is there a website that anyone knows of for these types of open-source curriculums? Feel like it would be nice to have a place where people could post these and you could reference them when you wanted to learn something in the correct order and with the best resources.

They’re much narrower in scope than a full curriculum (or even a course, for that matter), but Better Explained [0] has some very good overviews of math topics. They are a useful supplement I’ve come across repeatedly while searching topics I found challenging over the years. On the topic of open source learning, I take every chance I can to heartily recommend fast.ai’s course [1]. It’s a good intro to Deep Learning…

Perhaps more relevant for this topic is the computational linear algebra course from fast.ai:

https://www.fast.ai/2017/07/17/num-lin-alg/

It has a lot more detail on stuff like floating point storage, memory layout, sparse matrices, iterative methods, etc than most linear algebra courses, but doesn't go much in to proofs, geometric interpretations, and other stuff that's less needed for algorithm design and implementation.

(Disclaimer, I'm from fast.ai.)

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