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Back to Mathematics for Machine Learning: Linear Algebra

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11,458 ratings

In this course on Linear Algebra we look at what linear algebra is and how it relates to vectors and matrices. Then we look through what vectors and matrices are and how to work with them, including the knotty problem of eigenvalues and eigenvectors, and how to use these to solve problems. Finally we look at how to use these to do fun things with datasets - like how to rotate images of faces and how to extract eigenvectors to look at how the Pagerank algorithm works.
Since we're aiming at data-driven applications, we'll be implementing some of these ideas in code, not just on pencil and paper. Towards the end of the course, you'll write code blocks and encounter Jupyter notebooks in Python, but don't worry, these will be quite short, focussed on the concepts, and will guide you through if you’ve not coded before.
At the end of this course you will have an intuitive understanding of vectors and matrices that will help you bridge the gap into linear algebra problems, and how to apply these concepts to machine learning....

PL

Aug 25, 2018

Great way to learn about applied Linear Algebra. Should be fairly easy if you have any background with linear algebra, but looks at concepts through the scope of geometric application, which is fresh.

NS

Dec 22, 2018

Professors teaches in so much friendly manner. This is beginner level course. Don't expect you will dive deep inside the Linear Algebra. But the foundation will become solid if you attend this course.

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By Domenico D F

•Jan 22, 2023

Excellent course, give a fast and intuitive understanding of the concept that are below linear algebra. For people doing other kind of work, like phD in some other non-mathematical field, that somehow lack the mathematical back group I think is good place to start. Still need to see how those skill will test against the real world. But time wise is probably one of the best option. I also started with a book, Linear Algebra done right, but, even thou the concepts are way more deep in a book, I found that was taking me too much time to arrive at a reasonable understanding. So I opted for this course.

By Tim Z

•Mar 31, 2018

Actually I have learned linear algebra before but forget a lot, so I want to use this course to review it and help me prepare for the study of machine learning. As a computer science student(sophomore), I think the coding assignments are too easy for me. But it indeed introduce the core concept and equations in linear algebra, which are quite useful for future learning. In my opinion, freshman students or students just graduated from high school may feel more satisfied with this course. And it is better for students who have learned linear algebra before to find harder courses to learn.

By Harsh S

•Jul 25, 2018

Good course for your first step into machine learning. Very engaging. Great application with the PageRank problem. The course does dive into the core understandings of linear algebra and you do develop a sound mathematical intuition. The coding isn't very difficult and has been eased for non-programmers. However, what happened for a keen learner like myself is that I wrote code which I didn't understand very well myself, but still managed to get a full score. This made me a bit uneasy. Otherwise, an awesome course to get started on and it is possible to finish in two weeks.Enjoy!!

By Marc P

•Apr 19, 2019

Excellent course to refresh linear algebra basics, build intuition and see the subject from a machine learning perspective. I wouldn't recommend it for people that are new to the subject, since the pace is fast, much is omitted and the assignments aren't always easy. Every now and then, the calculations come before the intuition, which can be tricky to follow. However, most of the course is very didactic and the combination of videos and challenges kept me motivated throughout.

I suggest the youtube channel of 3Blue1Brown whenever you feel lost with the subject at hand.

By Kenny C

•Jul 10, 2020

The lectures from the instructors were well-thought-out and planned, which gave it a clear line of reasoning and allowed them to give good examples. However, some parts of the content are glossed over, especially with the introduction to matrices. The instructor does not define what a matrix is and how basic operations with matrices work, though this is done when they introduce vectors. Overall, I would have liked a more rigorous and mathematical explanation of the content, but the course does do a good job of building an intuitive understanding of the topics.

By Hamed K

•Apr 22, 2020

The instructors explained the topics almost clearly. I would say the assignments were a bit difficult and did not have any explanations by instructors in the videos. More importantly, the support of instructors in the forums is very poor. Many people have had issues but there has not been any answer provided by the instructors. The submission of the assignments were a nightmare since grading of the coding gives a lot of issues even if the assignment is correctly done. With more support by the instructors in the discussion forums could be a much better course.

By Kjell E N

•May 20, 2020

This was a really good refresher for material I learned long ago. The instructors were enthusiastic and engaging, and the production quality was good. The material is pretty abstract, however, and as with any brief course, it is difficult to develop a truly deep intuition about the subject without much further study and practice. I like that the homework was quantitative and required me to think carefully and practice the mechanics of doing the math. If nothing else, taking this course has me wanting to keep studying Linear Algebra!

By Kenneth B

•Jan 9, 2021

This course provides a good overview of the basics of linear algebra for machine learning tasks. I recommend the class and I'm glad I took it, but it could be improved by adding more thorough explanations for quiz answers. This would have let me better understand how to arrive at the solution to a problem.

I didn't have any Python experience coming into the class and made it through OK, but there were times where this lack of knowledge interfered with my ability to complete the Python labs (particularly the last one).

By Osaama S

•Sep 29, 2019

Instructors have done a really good job at introducing the fundamentals specially from a graphical point of view which allows you to build your grasp strongly around the topics in a way that is not accomplished in a traditional college classroom. However, I would say perhaps there could be more challenging questions on the real world applications of linear algebra in machine learning followed by in-depth step-by-step solutions in order to really get the application-based learning inside your meat.

By Pitiwat L

•Sep 14, 2022

Most of things are good, but there are few problems. First, there might be some problem in jupyter notebooks, I run almost 20 times with exact dame code but it show that I got 0/10. Second, in some parts, the LaTex code is not shown properly they are some ($$$ sign) that is very hard to read. Third, the instructors teach too short and provide little details. However, a good thing is they show the visual ways too manipulate fomulae that seem to be hard to imagine, but they make it lots easier.

By Fatma F E S

•Nov 8, 2022

Achieved the goal of allowing one to have an intuitive understanding of linear algebra.

The quizzes were challenging and very relevant to the topic covered; and in one or two cases they went beyond what was taught to allow you to challenge your understanding even further of how the topic at hand may be applied in different cases, so definitely appreciated.

The feedback on quizzes could do with some improvement as they're not always to the point.

Was definitely worth my time.

Thank you very much.

By Gabriel L S

•Aug 12, 2019

I like the the structure of explaining the theory using examples (in this case, geometric/visual examples). However, I would love to have further understanding on the basic linear algebra topics (or at least be linked to websites that explain this further) to allow flexibility to students like me who has zero knowledge on linear operations. Overall, I was able to overcome the challenged through self learning, understand the concepts well, and appreciate the applications in machine learning.

By Allan d Q

•Nov 13, 2020

I'll go through this one once again, I feel like I'm not fully comfortable with the content. I had to use loads of external resources in order to pass through the quizzes and some of them I guessed, I must say.

The coding ones were a bit easier since I'm a software engineer already but yeah, I definitely need to through it again but overall, I've discovered many new things that were unknown unknowns.

Thank you all for putting this kind of content online for everyone! Outstanding job!

By Yuriy G

•Jan 31, 2019

Thanks a lot for this course! The explanations and lecturer work were brilliant!

It's very good for introduction but it lacks a strict wording, definitions and some generalizations. Especially in the section of changing basis. When after considering a number of examples, I really want to move on to the general case.

Anyway, you've a made a great work because anyone without any preparation can get acquainted with very deep mathematical ideas.

By Kumar S

•Apr 14, 2020

This is a very good course and helped me a lot in getting started with going through mathematical concepts of machine learning. It has taught me lot oh Linear algebra stuffs in a very intuitive way. However the quality of assignments could have been better and some of the concepts that were important and needed more explanation was skimmed through rather quickly. However, I am really satisfied with the overall learning that i got.

By Nikita V M

•Feb 6, 2020

Excellent instructors and video quality. Some frustrating elements with assignments being either somewhat unclear or redundant. The only severe flaw was that grader feedback was entirely pointless, as it made no effort to even give an example of what went wrong. Simply saying that something was incorrect without providing, say, an example of the input matrix that failed, in no way helped advance my understanding of the problem.

By Leandro C F

•Mar 4, 2021

This is one of the best math courses I've took in Coursera.

20 years ago, I took linear algebra in my University. And now I needed to remember some of these topics. For this purpose, it is excellent. The way matrix transformations is addressed was new to me and make the topics very easy to understand.

Unfortunately, the topics of week 5 (eigenvectors and eigenvalues) were not so well taught as the topics of weeks 1 to 4.

By Alex R

•Mar 28, 2021

An excellent visuals of application of Linear Algebra. Some of the homework is not based on the material presented in the class, and requires you to go to external sources to learn more. When doing homework, sometime, it unclear what additional material you don't know and need to learn outside of the course work, to solve the homework. Other than homework, it's an great class to take! I've really enjoyed this class!

By Khubaib A

•Jul 27, 2020

Python. Python is needed. It'll be very hard to progress without that. Otherwise, the course is great. Instructors are good. Week 5 is sort of a stretch. The Page Rank Algorithm is not really explained well (some say that it is not explained completely) and dedicating an entire week to just eigenthings does not make a lot of sense. The exercises are good though. A good introduction to the basics of Linear Algebra.

By William L

•May 19, 2018

Video lectures are great and really help with understanding why you are learning the material and what the concepts mean. The programming assignments and quizzes are challenging. There were some cases where I did not understand the quiz question and did not know why I got it wrong or even correct if I guessed. Access to solutions after completing a graded assignment or even after the course would be beneficial.

By James G

•Apr 1, 2018

It's quite good. The material implies they are aiming to teach linear algebra and basic Python programming basically from scratch, but it goes over topics so quickly and skims over so many details that I suspect this course only works if you've studied much of it before. Even though I have studied much of this before I still had to go and find other sources of information, as the explanations here are so brief.

By Kitty

•Jun 12, 2019

Generally great course. Explanations are very clear. Cons: ① no textbook/slides/reading materials etc., have to take notes and screenshots for every single thing you want to record. ② The content is not enough. Way too less knowledge covered than college-level linear algebra course. I took this course to refresh my knowledge and it turned out that more than half of the contents are the ones I still remember.

By Mohamed H

•Mar 16, 2021

The course did a good job in building up intuition about linear transformations and change of basis. It's a useful review of the core of linear algebra and can be implemented in many fields. The programming assignments were very basic, so maybe a bit more challenging ones will be better. I didn't like the last module of the course about Eigen analysis. While the topic is very useful, it was a bit rushed.

By Amit A

•Aug 30, 2019

Eigenvalues and eigenvectors while explained conceptually very well, the jump to page rank and transformations using them was bit hand wavy. May be it is not that important or the topic is too complex. I think I have to go through it multiple times to get the gist of it once again. I might if there is real applciation of it in ML.

The course is still very good and thank you for sharing it with us.

By Grant T

•Jun 30, 2020

Without having taken a Linear Algebra course previously, I thought the course was worthwhile to introduce topics. However, I had to spend ample time researching outside of the course IOT learn. In addition, although I was introduced to many LA topics, I still need additional practice in grasping certain concepts. This course is a good introduction to topics you'll have to research on your own.

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