Back to Mathematics for Machine Learning: Linear Algebra

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10,879 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....

CS

Mar 31, 2018

Amazing course, great instructors. The amount of working linear algebra knowledge you get from this single course is substantial. It has already helped solidify my learning in other ML and AI courses.

EC

Sep 9, 2019

Excellent review of Linear Algebra even for those who have taken it at school. Handwriting of the first instructor wasn't always legible, but wasn't too bad. Second instructor's handwriting is better.

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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.

By Lizzie M

•May 25, 2020

It's a really good course with great tutors, really engaging and easy to follow. It can be very challenging at times if you don't come from a maths background. There are some assignments which are much harder than the examples in the lectures so some extra material to help you with those assignments would be great, otherwise personally they demotivated me. Other than that the course was good.

By Rob O

•Apr 10, 2020

Having last taken linear algebra many years ago this course was a welcome refresher. Overall the course is excellent with clear explanations, good examples, and opportunities to practice your newly learned skills. That said the last assessment on eigenvectors did not evaluate learning and skills as much as reasoning about special cases and focused on problems better solved computationally.

By Oriol C

•Jun 6, 2021

The course is good as a refresher and it helps learning the intuition behind some concepts. The professors are very likable and do their best to explain the materials. However it is not good if you are looking for rigorous explanation of the mathematics as they go very quick on most of the concepts.

Taken this into account I would still recommend it to get some quick grasp on the intuitions.

By Mackie Z

•Aug 3, 2020

I have experience with python numpy and pandas, so I found the assignments reasonable, but i think the programming assignments can be confusing to someone who has never coded before. There're a few times when I found myself lost in the instructor's explanation and needed to find more clarification online, but overall the videos are of great quality. It's a great course for self learning!

By Pavel S

•Dec 12, 2019

The biggest problem of this course is that dot-products are introduced before linear transfomations. I understood dot products through 3blue1brown videos and they are more intuitively explained as the product of the lengths of the projection and the vector projected onto. It is a subset of linear transformation a matrix vector multiplication where one of vectors is transposed.

By Alex H

•Jun 8, 2020

I'm sad, because I finished the course, but instead of a solid understanding of linear algebra, I mostly feel confusion and frustration from what I was not able to ask the professors. But overall, the instructional videos are high quality, and the quizzes were challenging. At least it forced me to think critically about the subject, so I don't think it was a waste of my time.

By Fang Z

•Jun 11, 2019

The course generally is good. However I think there are some problems in this course: 1. The course pace is too fast, some concepts are hard to understand with few minutes lecture 2. The after-practice didn't help me to boost my understanding to the lecture. Even after I finished the practice, I still wonder why this happens 3. The final quiz has too much calculations.

By Prasad N R

•Sep 30, 2019

I was expecting a lot from the course. But, it covers only the very basic portions. For example, I am not sure if I can start understanding the difficulties with normal equations and portions of linear algebra based on calculus. Also, it does not discuss parallelism of ML with linear algebra. I am not sure if this will help me read and understand Andrew Ng's ML papers.

By Musiboyina Y

•May 26, 2018

The course content was spot-on, covering some of the most important basics for math in machine learning. I wish there were more programming exercise based assignments and less hand-calculation based quizzes to make it close to real world applications. Overall, loved this course and highly recommend it to data science enthusiasts taking baby steps towards deep learning.

By s S

•Aug 5, 2018

This course has provided everything that it had promised. The professors of this course are really knowledgeable about the topics and the use of real life examples by them to explain each concept proves really helpful. Overall, this course would be a really good starting point for anyone willing to start their journey in the world of Machine Learning and Data Science.

By Jennifer J

•Jul 17, 2020

Great course, but difficulty spikes after the first few weeks and problems become much more challenging, albeit far more interesting though. The course reaches its peak when it challenges you on the interesting problems presented to you during the last few weeks. You may need to have some basic understanding of algebra and a bit of calculus too before starting.

By Divyang S

•Jul 28, 2020

Really Good course for people having some basic linear algebra knowledge. They could have done better on explaining some concepts rather than rushing through it... But a great refresher course... One recommendation would be to suggest good books for Linear Algebra that might be helpful for students who take this course, some book which can accompany this course.

By Vedhasankaran H

•Dec 31, 2020

Excellent Course Content and well presented. The instructors did a great Job in conveying the fine details . However The course should emphasize Python as a prerequisite and the instructors can include a lecture on "Basics on Linear Algebra with Python " in this course as the Assignments from Week3 through 5 involves applying Linear Algebra in Python

By Julio V

•Sep 27, 2018

I feel like some part should've gone a bit more in depth. Due to time constraints for the course, I guess that's why some topics where not developed further. Would be quite nice in these cases if you could point to other sources, books, etc. Or maybe do a compilation of sources based on what the students have used to get unstuck on particular issues.

By Régis M

•Dec 28, 2018

As paletras e numero de exercios foram muito bons. Porem o forum não é muito bom, existe questões abertas a 4 meses que ainda não foram respondidas, e muita repetição de duvidas.

Poderia ter apos os exercicios praticos, um video explicação de como resolver. Porque se a media é 80%, é presumivel que o aluno pode não saber alguma coisa e ainda passar

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