Back to Mathematics for Machine Learning: Linear Algebra

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9,931 ratings

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1,995 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....

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.

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 Ed E

•Aug 1, 2019

This course is excellent however it is not for the mathematically immature unless they are willing to put quite a bit of additional work in. Arguably it can be classed as "Beginners" but still, I can imagine many will feel lost very quickly. At one stage David Dye offhandedly mentions soh-cah-toa... and that really sums up a lot of what is required in terms of mathematical maturity - high school maths at a reasonable level.

Those that undertake the course should be assisted by referring to additional materials when they feel things are a bit of a struggle, I did, and this greatly helped, although my Maths was around UK high school level (in Algebra and Trig).

Overall first class and easily manageable with a little work!

By Dharma T N

•May 9, 2018

This is indeed one of the best math courses I have ever done in my life. This course changed the view I look at matrices and vectors. I have been 'transformed'.

The instructors were simply amazing. Totally loved every bit of the course. Amazing way to teach this math course, with proper motivation and intuition.

And for all the people writing negative reviews about no Machine Learning being taught in this course, it is clearly mentioned that this course teaches the math which is required for learning Machine Learning and not Machine Learning itself.

By Anonymous

•May 9, 2018

The content and the speed are not satisfactory.

The speed totally hampers the content, lots of things aren't explained especially after Sam took over in the last module.

Other than the first 2-3 intuition videos and the programming assignment nothing was good in the 5th module/week.

It was very very difficult to follow the page rank video. I still don't understand it. For eigen basis I had to refer to other material outside this course.

By Jeffrey J

•Mar 8, 2018

Course is titled incorrectly. The course has nothing to do with machine learning. It's mainly out of context symbol pushing (like most math courses).

I expect any positive reviews will be from folks who do not work as a practitioner in the field and just want to promote "good vibes". Beware if you're actually looking for contextualized understanding, as this is not the course for you (at least through the end of week 3).

By Nabil C

•Oct 5, 2020

First of all, the instructor clearly loves the subject he is teaching. You can tell immediately by the voice and the gestures.

Second, the fact that he is not a pure mathematician means he is constantly looking for the link between what he is teaching and practical examples. That's a must when you are teaching math to students intending to use it in real life (Machine Learning).

Third, there is a good structure to the material being taught, always building on what has previously been taught.

Fourth, is the amount of quizzes and exercises. Math can only be learned effectively if you keep challenging yourself in quantity and quality. Everyone remembers the quality bit, but some miss the quantity. Not this instructor I have to say. Congrats for that.

Fifth, intuition is being built from day one. Big applause for that as Linear Algebra lives and dies by the amount of intuition that's being put into its practice.

Sixth, my hat's off for the esthetic quality of the figures and exercises, and for their clarity.

Seventh, even for an engineer like me (graduated over 20 years ago I have to say) who's been best friends with Linear Algebra and Calculus for the 6 years I was in university (10 semesters + a final Master's thesis), this course wasn't trivial, and kept me making an effort at every bend, at every corner. This is something I am grateful for, as while I was refreshing concepts that I hadn't touched for 20 years now, I did have real fun.

Eighth, the coding examples are a magnificent tool that greatly helped strengthening some concepts (like Gram-Schmidth, etc.). Amazing job there.

Ninth, you can see how towards the end of the course, gears are shifted, pushing the student to get mental agility, and conveying the student the importance of intuition building (+ some algebraic symbolic manipulation) as opposite of focusing mainly on the symbolic manipulation. A good approach nowadays that computers do the computation for us, as opposite to what it used to be some decades ago. I really liked the fact that the instructors (Dr. Dye and Dr. Cooper) tried, both, to covey this very practical philosophical paradigm from day one.

My most sincere "cum laude" score for this course.

Nabil Chouaib.

By Timo K

•Mar 28, 2018

Pros:

Amazing explanations of the covered topics, extremely engaging teaching staff

Focusses on the right things

Good and enough practice problems

Great (albeit easy) programming problems

Cons:

Calculation of Eigenvectors could have been covered better in my opinion

A final handout for all the covered topics would be really nice

Overall a tremendous course if you want to brush up on linear algebra. To me LA was taught mostly doing rote calculations without motivating the concepts or explaining them geometrically. I had more than a handful of "oh, so that's how this actually works" moments. I feel like my intuitive understanding of linear algebra concepts has made a big improvement.

By Laurent G

•Apr 6, 2019

A very good introduction but some of important content need to use another provider (Kahn academy) to understand completly

By Ashley W

•Mar 31, 2019

Lots of unaddressed inconsistencies.

By Jorge N

•May 2, 2018

Mainly explains how to operate with matrices and vectors. Not how to use those in machine learning. If you expect to have a clear view of the usefulness of eigenvectors and eigenvalues in machine learning, this is not your course.

By Badrul I

•Feb 25, 2019

Not intuitive or well explained. Examples are horrible

By MARGARET P

•Jul 31, 2020

Why can't I give this course ZERO stars? Because that is what this course deserves.

The first course in the specialization was a train wreck. For starters, the videos were heavy on theory and light on examples, so when it came time to do the practice exams, each student needed to go to outside sources to learn, from the top, what they needed to do to complete the questions. This expectation is unacceptable. Secondly, no mention in the course information, videos, etc. was there any indication that there was coding. These coding assignments are delivered with no hint given as to what we would need to do, how, and why, which is entirely unacceptable. Lastly, the course creators are available nowhere. There are hundreds of questions on the forums for each week of each course, with not one answer coming from any of the course creators. I even went out of my way to find the email for the leading course creator and ask for additional resources/help but received zero response in return. I have been an avid supporter of Coursera for a long while now, but this specialization is terrible enough that I would consider never utilizing this site again. Mathematics for Machine Learning is an embarrassment to the entire service and devalues all of the work individuals have put into learning through this platform. It does this by diminishing the quality of the certificate by demeaning the level of competence acquired upon completion. If I were in charge of content, I would remove this specialization as well as thoroughly review all content published by the same institution. David Dye and the Imperial College of Londen should be ashamed.v

By Mary B

•Jan 29, 2021

I only completed three out of the five weeks of this course. Too many of the lessons were just a source of frustration for me. The instructor doesn't explain things very well. For example, with change in vector basis, he walked us through using the dot product and scalar values, but then added them up. Nowhere did he say the last part was just a check, and it had me confused for quite a long time. Then, with Einstein's Summation Convention, he doesn't really explain the subscripts and what rules there are for their use. Plus, it's hard to follow along because he says the math out loud, then just writes down the answer. Since this is new to me, it would be good to see it written out, like | (1/2)(-2) + (-1)(4) |. Far too often, I had to rely on other resources to get enough of an understanding to complete the quizzes. By the fourth week, I started just skipping to the quiz and finding other resources to teach me how to solve the problems. Then, I decided to just give up entirely. And finally, there were issues with the auto-grader. With one, I needed to write out the values as 2.0 instead of 2, but there was no mention of needing this precision. With another, it was A[3, 0] (with a space) instead of A[3,0] (without a space), even though the provided code used A[1,0] (without a space).

By Rob E

•Aug 11, 2020

I learned a lot of valuable concepts in this course. But, the pedagogy is very poor in my opinion. The videos are taught by Professor Implicit, the notation is inconsistent and confusing, and I never saw even one response to questions from the instructors.

Seems this is for people who have a very strong math background even though it's marked as an introductory course. It took me several months to complete this because I had to go through almost all of the Khan Academy Linear Algebra course to understand.

Great concept and content. But, responses to student questions and better explanations would help a lot.

By Marco G

•Nov 10, 2019

Great class to build an intuitive understanding of the concepts. The topics covered are not as many as in a serious course in linear algebra, but the ones covered really help you get to a genuine understanding. The assignment basically consist in rewriting in python what you see in the slides. If you are familiar even at a very basic level with Python, it will take you less than 5 minutes to complete the assignments, they are not challenging at all in that sense. But they do help visualize what is taught in the vides, which I guess is the purpose. To conclude, I would suggest paying for this course only if taking the full specialization, otherwise simply watch the videos for free!

By John F

•Jun 1, 2019

This course is the first of 3 Machine Learning Math courses in this specialization which I am taking because I desperately need it as a refresh and as preparation to take Andrew Ng Machine Learning Course in the very near future. So I am 1/3 of the way there to being ready to take Andrew Ng famous and highly regarded Machine Learning Course. I began taking it but after 3 weeks, It became apparent that I needed this so that I can actually grasp and understand the material. I am so looking forward to starting it over again here shortly after I finish these next 2 fundamental prerequisites as I regard them

Kind regards,

JeanPierre (John Fisher)

By Surendar R

•Jul 21, 2019

This course is absolutely stunning in terms of explaining mathematical concepts. I personally have been out of hands-on touch with mathematics for a decade, and by going through these videos, tutor has been absolutely spot on for me in bringing back my mathematical memories. Would highly recommend this course for anyone wanting to enhance their mathematical skills or brush up on mathematical concepts before doing deep dive in machine learning concepts. It really connects and I am enjoying this. Thanks for all these wonderful lectures.

By Praveen D

•Feb 2, 2019

I found the course very interesting and useful. I really liked the approach of relating Linear Algebra to practical use. Traditional approach to teach Linear Algebra (which assumes some familiarity with Modern Algebra) may not be for everyone and the approach taken in the course will find much acceptance among curious learners. Thank you so much for putting this course together. May be, putting together a more detailed and longer course on Linear Algebra will be good idea - if it happens, i will be the first one to enroll !

By Daniel R

•Jun 4, 2019

I have tried Linear Algebra via Gilbert Strang lectures before but found them unengaging because they are so abstracted. Here we see how the linear algebra applies directly to pageRank, which I found a cool example.

In general the questions allow for a good practice and build up, and I really appreciate the lecturers appreciation of the fact that hand-written calculus is becoming a thing of the past, and so we should focus on the big ideas behind the methods that are now so standardised for processing linear systems.]

By Rui_Lian

•May 24, 2018

Many thanks for David and Samuel! I've been struggling with linear algebra for quite a long time. I can do the math, but I get lost when I try to use linear algebra to understand something in statistics and machine learning. The intuition based approach is perfect. I like the apple-banana example, I like the transformation and visualization of eigenvector in 2 dimension. Also, the page rank case is quite cool and thought provoking.

I think I will stay on this series for following two courses.

Thanks again!

By Wayne C

•Mar 29, 2019

Best presentation of fundamental Linear Algebra I have ever seen, hands down. (I'm an old-timer, reviewing this material to get up to speed on Machine Learning and Data Science.) While teaching the mechanics, the concepts behind them are always reinforced. Thank you for presenting this material in such a meaningful and digestible way. I also greatly appreciate the reverse-transparent-whiteboard which to me is highly preferable to the other methods I have experienced in online courseware.

By Xiaojun Y

•Oct 8, 2018

This is such a wonderful course. Two instructors explains complex concept with clarity and enthusiasm. They explained linear algebra from a different perspective. When I learned in college, I was taught to remember lots of definitions and concepts, but in this course, they teach you why we do certain steps not just how to do. However, I want to remind people who are interested in this course, it is not for beginner or who wants to learn linear algebra, instead of linear algebra for ML.

By Jonathan F

•May 20, 2018

Excellent introduction. For me, as someone who had studied vectors and matrices at school, decades ago, it was wonderful to go back and re-learn this stuff in a different way. This course is much more focused on the meaning and usefulness of these things, rather than just learning how to do the maths. The first 3 minutes of the session on eigenvectors brilliantly showed in graphical form what they really are, something I'd never really grasped at school. Recommended.

By Raymond I M J

•Feb 2, 2020

An excellent breakdown of linear algebra and the tools and processes that it takes to perform these operations. The lectures give you a good understanding of the concepts of vectors, scalars, dot product, matrices, and eigenvalues and vectors. I would highly recommend this course for anyone who is needing to understand how linear algebra can be conducted via computers, while still grasping the underlying concepts that make one proficient at linear algebra.

By zachary k

•May 10, 2020

I had previously taken linear algebra, but this was a good refresher. The pace of this course is quite fast for 5 weeks, and the course does not dive into any proofs. It may be useful to get some outside supplements to get through the materials. I really enjoyed the way that the concepts were explained and presented such as eignvalues/vectors. They help provide some intuition instead of simply presenting the formula or grinding through proofs.

By Nelson F A

•Apr 25, 2019

This is a great course! Be advised: It is very challenging and will kick your butt if you haven't seen much linear algebra before. The content in the course won't always be enough to solve all of the assignments. But look into the forums and use some other sources and you will succeed in this course. Overall I am glad I took it even if it will take a little longer until I can say that I master everything that was covered in the course.

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