Back to Mathematics for Machine Learning: Linear Algebra

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9,911 ratings

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1,993 reviews

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 Patrick B J

•Jul 25, 2018

Hands down the worst course I've ever taken in my life! Poorly put together and extremely short videos that don't provide an adequate amount of knowledge especially in relationship to the given quizzes. I truly hope this course is removed.

By sitsawek s

•Sep 13, 2018

Quite difficult for learner who didn't know about linear algebra.It jump and few example and skip a lot of part for understand.But good for recall.

By Parichit S

•Aug 25, 2020

It's an amazing course but apart from the feedback that I have in the post-course survey - I would also like to share the following things.

1) In the quiz on 'Eigenvalues and eigenvectors' in the Week-5 module -- I personally faced a lot of problems in completing the quiz. I understand the concepts pretty well from the lectures but still, I could not figure out the questions in this particular quiz. Particularly the questions about finding the effect of using a particular Link matrix on the eigenvectors. These questions were not easy to answer as intuitively speaking I did not learn how to interpret the meaning of different values in the eigenvectors matrix to answer those questions forex. it makes the eigenvalues small or It makes the eigenvalues we are looking for larger.

Overall - it is a really useful and much-required course to fill in the gap between the mathematical fundamentals and the practice of machine learning. I am glad that the Professors came up with this idea to design this course.

By Stefano C

•Apr 23, 2021

Thanks for this wonderful learning opportunity! This is the first math course that I've succesfully completed and I'm quite proud of myself. Teaching material is very clear and nicely structured - I've shared the first video about Eigenvectors and Eigenvalues with many people: it's illuminating -; also, quizzes and programming assignments really helped in understanding some of the main concepts. Actually, the nice balance among theory, hand-made calculations, geometrical examples and programming assignments provides a valuable way to learn from multiple perspectives.

Apart from this. I realize that I still have to completely "digest" some of the concepts that have been introduced here. In other words, I've learned to use them decently but for sure I need to reharse some of them in order to fully understand their meaning. But, by the way, this is fair enough: linear algebra is a complex and deep subject and five weeks are probably not enough to fully understand its main principles.

By Bram D

•Apr 29, 2020

In reviewing this course it is important to state what this course is and what it is not. It is not an in-depth formal introduction to the mathematics of linear algebra. For those who are looking for that, the course simply does not deliver. Secondly, while it is technically possible to complete this course without any beforehand knowledge of the topic, I think this would be incredibly challenging to do. Indeed, the course is not intended to be a first primer in linear algebra. The ease with which the instructors just juggle the cosine rule, or calculate the inverse of a 2 by 2 matrix indicates that they do assume you know such things. So also absolute beginners will be disappointed with this course. However, if you have had linear algebra in your past, and you are using this course to refresh your mind, it is absolutely brilliant. I can confidently say that nobody has ever presented this material to me in as intuitive a way. A well deserved five stars from me.

By Juan R

•Mar 27, 2021

The course touches base in the main topics of Linear Algebra utilized in ML. I took this course at the same time with a ML one. I hadn't had linear algebra in University and the contents of this course helped me get through many bottlenecks in the ML course (which obviously takes for granted Algebra).

The videos are very well produced, animations look great and explanations are crystal clear.

The instructors present the topics in a friendly way and always keep the focus on the concepts rather than on manual calculations (of which you won't be doing much in ML...).

The only downside is that watching videos more slowly (0.75x) is not fluent. I don't know if the issue is on my end or if the videos don't have enough frames per second.

If you have no Linear Algebra basis and are planning to do ML, It's definetely worth it taking this course.

By John T S

•May 7, 2020

Above all I found this course well oriented toward becoming useful. The conscious avoidance of heavy mathematical description was a good choice for the online medium. As a learner, I suppose I might have learned better with a bit more... testing, I suppose is the word? To work through a few more examples? But actually, a few well-chose gulfs between the presented materials and (especially the last) testing materials brought some useful questions and explanations. The eigenvector materials are conceptually slippery. Maybe one more example to work through, with clumsier numbers? Although, maybe that would have been boring and confusing...

Which is why I'd give the course five stars. It makes complex material usefully simple, while acknowledging that some things are of necessity left out.

By Hansa A

•Jan 25, 2021

This course is an excellent course to learn and apply Linear Algebra to algorithms and day to day life problems. Typically linear algebra is a very hard course in undergrad life but after this course I have gained a solid knowledge in linear algebra. I think the main reason for this is that in this course the instructors have a different approach when teaching this course. They visualize entire concepts of linear algebra so that we can understand the topics very clearly. This is the way to teach linear algebra. There is no point of doing 100s of problems to face an exam, the only thing we need is to visualize and understand the concepts of linear algebra. Thank you Imperial College for doing that. This course was extremely important for my further studies. Do it, you won't regret it.

By Ritobrata G

•Jul 12, 2020

As a student with Physics background, I though that this course will be a quick recap for me. But was I in for a surprise! This course completely changed how I see matrices and vectors. The instruction videos were very edifying. The teachers were great. I am fervently thankful to Imperial College, London and Coursera for such a great course.

There could be some improvements- the assignments felt ambiguous at times. They were not clearly worded and what was expected was not clear. And there could be some very practical excercises in ML where the concepts I learned could be directly applied.

A special note- the instructors were great. Their method was well thought, cordial and the videos were very informative.

By Mia C

•Aug 2, 2020

I have just completed the first of the 3 courses in this series. First of all, I must thank Professor Dave for the excellent efforts he put into delivering those first 4-week of fun and excellent topics. You have made it so interesting to me that I would love to know more about linear algebra. (*** Not only that, you have taken us on a informative journey of shopping for apples, bananas, and carrots to some visits to bears! : ) : ) ***)

For week 5, Professor Sam had given me some excellent materials as well. I look forward to taking the second course in the very near future.

Both professors are so smart and clearly great teachers! I feel so lucky to have stumbled into this course!

THANK YOU BOTH!!

By Warul K S

•Jun 28, 2020

The representation of mathematical concepts as "tools" to solve practical problems was beautiful and enabling, the way the instructors build our intuition rather than providing us with a bland approach to simply solving mathematics questions was phenomenal, the structure of the course was definitely first class as one would expect from Imperial. We were guided through the assignments but not fed the answers, our understanding was tested and additionally built upon through each exercise. Overall, I would recommend this course to anyone studying the subject in college or desiring to build a solid mathematical foundation for machine learning or even simply to appreciate the beauty of mathematics.

By VARUN S

•Sep 14, 2020

The reason I liked the course is its focus on important topics. Many complain that it was not for beginners and I understand the frustration. They shift gear in some assignments, but you have to put time to explore and self-study the material to move ahead. That is how the real learning happens. I think there was an advantage of not having a specific reference book. I have tried other LA courses and these books can absorb all your time and you may find yourself at the same place after 6 months. On contrary, this course forces you to go out and study only the topics you are struggling with. All in all, one of the best MOOCs I ever attempted ... Cheers!

By Anikesh M

•May 16, 2020

The course is extremely interesting and fun to do. Instructors have put a lot of efforts to make some complex topics seem easy and engaging. I could relate the calculations being implemented into practical ML applications. But i would also like to add that the last module of eigen-values and eigen-vectors gets very confusing especially the page rank algorithm and the quiz of eigen values and vectors..If the instructors could add a video or two to explain some more concepts, the course would become a perfect package even for a beginner.

AT LAST I WOULD THANK IMPERIAL COLLEGE LONDON FOR MAKING A FABULOUS SERIES. I REALLY LOVED LEARNING FROM YOU.

By Iacopo C

•Aug 22, 2020

Its purpose is to build the intuition behind the fundamental, important topics of Linear Algebra required in Machine Learning, it aims to develop the insight required to access other courses on Machine Learning Tools and as such it does an amazing job.

The clarity and enthusiasm of both the instructors is priceless and when a subject like this is communicated so effectively it makes a huge difference.

If what you're looking for is an understanding of the concepts that are the foundation of ML together with some rigorous exercises that will help you solidify you knowledge then I definitely advice on enrolling into this course.

By Andrew K N

•Feb 21, 2021

I have changed my opinion of this course. I am now at almost the end of the part three of the course, the PCA. and I have learned a lot. David introduced very important concepts of linear algebra in this part and this was really important part of this course.

One thing I have learnt from the course is to pay attention, take notes, pause to understand what is being taught. This enabled me to learn a lot and get the best out of this course.

Sometimes when a quiz seems too difficult, its ok to leave it a little and continue with the course. it gets easier to do it after a few more steps are taken forward.

I am truly thankful!

By aborucu

•Jun 5, 2021

ınstructors are engineers rather than mathematicians. This is very valuable because their pure focus is on application of relevant subjects rather than pure math point of view. of Dissecting relevant topics and applying them was a gem for me, rather go through 500 pages abstract algebra course without being able to tell whether I will use them in ML and if so where. One who has some background in LA will spend more time on course material, otherwise be prepared to watch some additional tutorials on youtube regarding subject matter. But instructors make this clear upfront and also provide links as well.

By Soumya A

•Jul 22, 2020

The course is great especially for a brush up of first year concepts for someone like me, but I couldn't help smiling throughout after realizing that the way this entire course series is presented is by reflecting the video lectures while they write on a transparent board about a vertical mirror plane. Although this must have been rather simple to implement, the idea is something incredible to my mind. Classic college education never exposed me to the ideas and a need to 'build intuition' for things like this course has. Kudos, professors!

By Hasala S k G K

•Sep 7, 2020

Excellent course! I serve in academia with a terminal degree in mathematics, but yet I learned many interesting connections specifically aligned with applications. This course is designed in a way it can be easily followed by anyone with a basic mathematical background but, yet can equally be enjoyed by someone with a strong mathematical background. After taking this course, I got motivated to enroll in 'Multivariable calculus' and PCA to complete the specialization. Thank you all who put the course (and the specialization) together!!!

By Cristiano M F

•Nov 16, 2020

Fantastic course. Much like what the reviews I read had anticipated. It is rigorous, the professors are competent and empathetic, and I feel they combined the right amount of theory with lots of practice (including on programming which was a first for me). Finally, they also made it clear that this is not a college-level course on linear algebra but instead a course on linear algebra that is specifically applicable to machine learning (as its title suggests) which is exactly what I was looking for. Thank you, Imperial College London!

By Aditya P

•Apr 27, 2020

I found this course excellent. For quite a long time, I have been struggling to understand what Eigenvectors and values mean and why do we bother to focus so much on Orthonormality. This course dealt with these concepts in a simple and lucid manner. It built the necessary math and intuition, which I liked the most. Also, this course really explained well why Matrices and its knowledge is important as it is useful in so many applciations. I am happy with the course and expect the same utility from the next course in the specialization

By Battal U

•Dec 23, 2020

Course is not boring from start to the end and course teacher are really good at speaking and teaching. They have great passion and they're fun. I like them a lot. I hadn't hard time to learn and make progress. Course is also very informative and made me passionate about expand my informations about the Machine Learning and other ares connected with Machine Learning like Data Science. Again I am thankful to everyone who made this course accessible to me and people who passionate to learn about Machine Learning core concepts!

By Soumyadeep S

•Sep 24, 2020

Both the professors right from the very beginning were not only very knowledgable but the way they delivered the lectures, it was really great. From the transformations to the rotations and shears, to the concepts of eigen values and page rank, this course is just so satisfactory for those who love mathematics . I learned a lot of things from this course, I started looking at vectors a lot differently. I would like to thank both the professors from the bottom of my heart for delivering such beautiful concepts.

By Mikhail D

•May 8, 2020

I see why some people are unhappy with this course (may be difficult to follow if you haven't seen Linear Algebra before / assignments are sometimes confusing), but I personally loved it. I took this course as a refresher for the main Linear Algebra concepts I last studied almost 10 years ago and the lecturers did a great job presenting the material in a very visual, intuitive, and over high-level way, making sure that you really get a feel of the main concepts instead of being buried in notation and formulas.

By Pieter t H

•Jan 6, 2021

This 5-week course, which can be completed in the evenings of one week, quickly give me intuition about matrices/linear algebra and their use in machine learning. Also, it's a step toward understanding PCA/ dimension reduction. The teachers are really good in explaining the difficult material, and there are enough short tests to practice. I recommend the course to all data scientists who are already able to pick a prediction algorithm with high accuracy, but want to understand the math behind it better.

By jie

•Jun 5, 2020

This course is a great introduction course to linear algebra. I am a quantitative finance guy and, to be honest, already forgot almost 90% of linear algebra I learned in college. It is always a little painful for me to code matrix multiplication during my work. I found this course before I went to amazon to buy a text book. This course saved me so much time and I really learned what I need to learn. Thank you so much.

The only con of this course is that: the python coding assignment is too easy.

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