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Introduction to Applied Linear Algebra: Vectors, Matrices, and Least Squares

vmls-book.stanford.edu

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Re: Introduction to Applied Linear Algebra: Vectors, Matrices, and Least Squares

#81

Post by hackermailman »

vark90 wrote: post #57
hackermailman wrote: post #17

Earlier quoted context omitted.

There's a practical course for this http://www.datasciencecourse.org/lectures/ anything you don't know, like linear algebra, look up the topics here for a 1-2hr crash course https://www.youtube.com/playlist?list=PLm3J0oaFux3aafQm568bl... There's a playlist for a math background in ML for anybody who wants to try a more rigorous ML course https://www.youtube.com/playlist?list=PL7y-1rk2cCsA339crwXMW... More information…

How useful do you think is studying general statistics from, for example, OpenStat vs. directly learning from ML-related courses like the one you mentioned?

If you scroll down this channel's videos you'll find lectures (36-705) that cover Chapter 1-12 in the book All of Statistics by the author of the book https://www.youtube.com/channel/UCu8Pv6IJsbQdGzRlZ5OipUg

I like the specific ML material since its usually sliced into a semester worth of material you can finish in reasonable time, most of these courses assume a background such as All of Statistics book and OpenStat is fine too for this.

Re: Introduction to Applied Linear Algebra: Vectors, Matrices, and Least Squares

#82

Post by chengiz »

VikingCoder wrote: post #2

I'm going to complain about this every chance I get. A 2D vector, we generally store as [x, y, 0]. What's the extra 0? The homogeneous coordinate. A 2D point, we generally store as [x, y, 1]. That extra 1 is the homogeneous coordinate, and since it's there, it means "and apply translations!" If I have a 2D transform, I put the translation component in the last row or column, depending on if you pre-multiply or post-m…

With due respect, who is "we" and what are you talking about? The book does not as much as mention a homogeneous coordinate and uses 2-arrays for 2D vectors.

Re: Introduction to Applied Linear Algebra: Vectors, Matrices, and Least Squares

#83

Post by muhneesh »

kharak wrote: post #37
muhneesh wrote: post #4

I'm e-learning Linear Algebra right now to have a good math foundation for Machine Learning. I was a History and Sociology major in college - so I didn't take any math. If you are like me, and working off an initial base of high school math, I would recommend the following (all free): Linear Algebra Foundations to Frontiers (UT Austin) Course: https://www.edx.org/course/linear-algebra-foundations-to-fro... Comments:…

Out of curiosity, do you feel you can compete with people who have advanced degrees in more quantitative sciences? Although I'm in the process of plugging several holes in my own math education, I don't believe I'd be able to get any interesting, ML related jobs. I also don't see myself able to perform well in comparison, given that I lack the mathematical intuition one builds after several years of (almost) daily pr…

The direct answer is - not at the research level but yes, in terms of application as the field matures and abstracts over time.

There are also adjacent jobs to ML engineer (product management and so on...).

Re: Introduction to Applied Linear Algebra: Vectors, Matrices, and Least Squares

#84

Post by karlmcguire »

k__ wrote: post #54
impendia wrote: post #48

Earlier quoted context omitted.

That's another thing I observed teaching calculus: a lot of students who have problems, are having their difficulties with the algebra they supposedly know, and not so much with the "new" material. In theory, we expect students to already be fluent in this sort of algebraic manipulation; in reality, we recognize that a calculus class provides our students an opportunity to improve at this. I'm not sure I have any sug…

Thanks. I successfully finished my CS degree. But I often have the feeling that my math problems are getting in the way of getting on the next level, hehe.

> But I often have the feeling that my math problems are getting in the way of getting on the next level, hehe.

Same here. I hate finding amazing CS academic papers and trying to implement them, only to get stuck at some high level math formulas.

Some of the best software engineers I know went from a math background to software. I guess I'm going to have to catch up.

Re: Introduction to Applied Linear Algebra: Vectors, Matrices, and Least Squares

#85

Post by muhneesh »

roymurdock wrote: post #61
muhneesh wrote: post #4

I'm e-learning Linear Algebra right now to have a good math foundation for Machine Learning. I was a History and Sociology major in college - so I didn't take any math. If you are like me, and working off an initial base of high school math, I would recommend the following (all free): Linear Algebra Foundations to Frontiers (UT Austin) Course: https://www.edx.org/course/linear-algebra-foundations-to-fro... Comments:…

Would be interested to hear why you’re studying machine learning. Do you see important problems you think it can solve, are you looking to make more $$ as an ML data scientist, or just generally interested in stats/data?

Part of a broader effort - I committed to learning to code about 3 years ago. At that point in time, I didn't really know why I was doing it... really out of curiosity. I kept going because it was addicting, and really an antithesis to my day job at the time (investment banking) - which I felt was corporate / bureaucratic and unintellectual.

That said, eventually, I want to start a startup. I'm building out small side projects now. I'm generally comfy with web + mobile dev, and I wanted to upskill in a "newer" technology that was more "mathy".

Re: Introduction to Applied Linear Algebra: Vectors, Matrices, and Least Squares

#86

Post by all2 »

muhneesh wrote: post #85
roymurdock wrote: post #61

Earlier quoted context omitted.

Would be interested to hear why you’re studying machine learning. Do you see important problems you think it can solve, are you looking to make more $$ as an ML data scientist, or just generally interested in stats/data?

Part of a broader effort - I committed to learning to code about 3 years ago. At that point in time, I didn't really know why I was doing it... really out of curiosity. I kept going because it was addicting, and really an antithesis to my day job at the time (investment banking) - which I felt was corporate / bureaucratic and unintellectual. That said, eventually, I want to start a startup. I'm building out small sid…

I bet you could flow-chart your entire firm into a process that's mostly automated. Something like wealthfront, maybe?

Re: Introduction to Applied Linear Algebra: Vectors, Matrices, and Least Squares

#87

Post by CamperBob2 »

School-Cotton wrote: post #66
CamperBob2 wrote: post #55

Earlier quoted context omitted.

It's right there in the sentence you quoted. True enough, thanks -- fixed. Still a completely bogus definition.

The definition (calling those unit vectors which are members of the standard basis “standard unit vectors”) sounds perfectly reasonable to me. You haven’t given any good reason why you think it’s “completely bogus” or “plain wrong”.

What is your personal definition of the term "unit vector?" Do you suppose there's a reason why no other textbook or Web site defines it the way these authors do?

Are there only N unit N-vectors, as the book says, or are there an infinite number of them?

Re: Introduction to Applied Linear Algebra: Vectors, Matrices, and Least Squares

#88

Post by all2 »

cultus wrote: post #76
syntaxing wrote: post #45

Applied linear algebra is such a great idea. Linear algebra is relatively easy to understand and used everywhere. But the material is so damn boring since it's a lot of arthimetic. Even the homework problem is boring since there is no specific purpose.

Typical LA courses in math departments have a bizarre focus on being able to do Gaussian elimination by hand and stuff like that. It's not particularly useful or even mathematically interesting. LA courses would be so much more useful if they just stuck to theory and only had computer applications.

I found knowing the mechanics of Gaussian elimination to be really helpful when learning about algorithms like SVD or using Householder transformations. Knowing how the matrices became triangularized gave me something to hang the new information on.

Re: Introduction to Applied Linear Algebra: Vectors, Matrices, and Least Squares

#89

Post by VikingCoder »

chengiz wrote: post #82
VikingCoder wrote: post #2

I'm going to complain about this every chance I get. A 2D vector, we generally store as [x, y, 0]. What's the extra 0? The homogeneous coordinate. A 2D point, we generally store as [x, y, 1]. That extra 1 is the homogeneous coordinate, and since it's there, it means "and apply translations!" If I have a 2D transform, I put the translation component in the last row or column, depending on if you pre-multiply or post-m…

With due respect, who is "we" and what are you talking about? The book does not as much as mention a homogeneous coordinate and uses 2-arrays for 2D vectors.

I'm off on a tangent unrelated to the book.

"we" is computer programmers who deal with vectors and points. Mostly graphics, physics, games, etc.

Re: Introduction to Applied Linear Algebra: Vectors, Matrices, and Least Squares

#90

Post by mindcrime »

impendia wrote: post #48
k__ wrote: post #44

Earlier quoted context omitted.

I was really bad at rearanging terms/formulars and this came up in calculus exams all the time, but not so much in linear algebra exams.

That's another thing I observed teaching calculus: a lot of students who have problems, are having their difficulties with the algebra they supposedly know, and not so much with the "new" material. In theory, we expect students to already be fluent in this sort of algebraic manipulation; in reality, we recognize that a calculus class provides our students an opportunity to improve at this. I'm not sure I have any sug…

That's another thing I observed teaching calculus: a lot of students who have problems, are having their difficulties with the algebra they supposedly know

A. You're not alone. In the first video of his Calc I series, Professor Leonard cracks that "Calculus is the class you take to finally fail Algebra".

B. This is hardly unexpected, especially if there's any gap at all between taking Algebra and taking Calc. The simple truth is, you forget material you don't use. And most people don't use a lot of algebra in their daily lives. If even a semester or two has passed since you took algebra, you're almost certainly going to have forgotten a lot of it, unless you made a very pointed effort to keep practicing that stuff and focus on retention.

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