Back to Mathematics for Machine Learning: Linear Algebra

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9,927 ratings

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1,994 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.

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.

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By Sébastien W

•Jun 22, 2019

The perfect dosage of the key elements in linear algebra to mastering the concepts of machine learning. The course leaves you with a clear intuition for vectors and matrices and how these objects can be manipulated, and most importantly why these objects are fantastic. I am an immunologist with a little background in machine learning and my last studies in mathematics taken 15 years ago, but this course has the perfect level I need.

By Burouj A

•Jul 6, 2019

This course was like God-gifted.

I had just finished my 2nd sem at college(BTech) and we had Matrices in the syllabus so I knew how to calculate (just calculate -_-) eigenvalues, vectors and so on but I just saw them as numbers. At my college, we were not given such geometric insight and when I learned it through this course, MY GOD was I blown away.

I feel so lucky to have found this course! I learned A TON of stuff.

Thanks!!

By FRANCK R S

•Apr 15, 2018

I took a great pleasure to study this linear algebra course, teachers are very talented since their way to explain mathematical concepts make it very easy to understand , in fact with this particular amazing approach I changed my perception about learning math and sciences in general. I do recommend this course if you look for a global overview of linear algebra for direct application in machine learning or computer sciences!

By Karandeep

•Oct 9, 2020

This course is great for those who want to understand the geometric meaning of linear algebra. Really loved the course videos and quizzes. Just one suggestion - Coding assignments should be bit more challenging as this course is targeted around ML, maybe some small Kaggle like project at the end of course.

By Siddhant J

•Apr 13, 2020

Excellent, crisp and to the point. Instructors made the concepts way to easy to understand. Enjoyed my time learning from them and ofcourse relevant material was provided.

By Michael P

•Jun 27, 2021

I think Professor David Dye's Linear Algebra video is the best course. It's much more clear, intuitive, and focused in the machine learning domain. I like it so much!!!

By David S

•Jan 1, 2021

A good value, well organized, with many exercises for practice. Effectively uses visuals, and contains the occasional very creative example.

Some caveats

a) this course is not for the absolute beginner. You'll need secondary / high school math, and basic familiarity with python

b) understanding linear algebra at this level is a second year full semester course at university. So if you want to understand the concepts - rather than just get the certificate - be prepared to use outside resources and invest considerably more time than advertised. Some linear algebra topics are skipped (cross product), and others are not well integrated into the course (Einstein summation)

c) while linear algebra is central to understanding machine learning, there are very few machine learning applications in this course.

And finally a small annoyance: I wish the instructors would get out of the way of the whiteboard at the end, so I could get a screen capture.

Overall, a worthwhile course.

D

By khaled W S

•Mar 25, 2019

totally enjoyed it. requires a bit of side research as any online course would. some of the quizzes were not directly related to the video that preceded them as one would expect. However, a fun course and covers a lot of important basics for it's relatively short duration.

By JUNXIANG Z

•May 17, 2019

This course reviews the essential concept of linear algebra in the context of machine learning. However, it would be much better if it provided more optional exercise and reading materials.

By Ralph T

•May 4, 2019

decent course. It gives a good enough background to understand the mathematics necessities of many areas of data science. could be more thorough and dive deeper into some of the content.

By Mark J T

•Aug 2, 2019

Good course because it shows how to understand geometrically, things that I had hitherto only understood computationally.

By Philip A

•May 16, 2019

Excellent Instruction

By Neel K

•May 10, 2020

For the most part, I enjoyed this course. Most of the math explained is fairly easy to understand. They cover the fundamentals of linear algebra, and provide plenty of assignments and practice exercises to test your knowledge. However, some of the video explanations are extremely confusing and feel rushed. For example, some videos in Week 4 and 5 like Reflecting in a plane using Gram-Schmidt and the PageRank algorithm were so hard to understand that I had to learn about them from elsewhere on the internet (I used MIT OCW a lot). This isn't very convenient, especially if you're paying for the course. Furthermore, I felt like more videos explaining the applications of linear algebra in machine learning could've been made, and the ones that were already made could've been made in more detail (for example, the term 'span' was never formally explained). Lastly, I would've loved it if there was another week dedicated solely to introduce the coding bit, because it's really difficult and takes a while if you have little or no prior experience in python. All in all though, I enjoyed this course, and I would recommend trying to complete both Linear Algebra and Multivariate Calculus in one month, because it's not worth paying more than that.

By Maytat L

•Nov 20, 2019

Challenging course. Much more difficult that I expected. It took me 7-9 hours a week. The overall course material itself was good building-blocks to further understand application of machine learning. However, explanation in some topics should have more detailed explanation and examples to further understand the concept. There were many times, I need to re-watch each video over and over again, paused it, and figured things out on my own. The programming assignments were the most challenging task. I just began to learn Python and found it very difficult because there were so many codes I haven't learnt before. I think for those who has not learnt Python at all may find really really difficult to pass the assignments.

By Peter B H

•Nov 26, 2019

The content was good, but a couple of times what was said didn't gel with what was being drawn/written/done. Since I'm learning, this took me longer to double check when I misunderstood something whether it was the concept or a mistake in the delivery.

By Pedro C O R

•Aug 1, 2019

The topics could be improved in the way they are presented. I always had to search for additional material.

However, the course is okay, it could be better, the forum is not that active, and some assignments are good.

By kai k

•May 5, 2019

many of the activities are excellent, but videos hard to follow along to at times - play them at 0.75 speed if you can. Also, the faculty is not super responsive it seems on discussion boards creating some confusion

By Girisha D D S

•Aug 27, 2018

Although the course content is good, I feel it could have been done better. I enjoyed the multivariate calculus course compared to this course.

By Maximilian P

•Dec 12, 2018

Some exercises are completely incoherent to the preceding videos, which makes it very difficult to solve them. very frustrating

By Dr. V N R

•Dec 9, 2020

Assignment makes frustration and not able to concentrate on teaching content

By Amit V

•Sep 8, 2020

1.) This is definitely not a course for beginners, especially if one does not know how to code OR if he/ she is weak in coding.

2.) As far as lectures are concerned, the faculty members/ lecturers are energetic. While some topics have been explained really well, many topics are either left without much explanation. There are some occasional mistakes on the part of faculty, which must've been edited and rectified. They have done good job in converting the lectures in to text. However, there were some mistakes in those texts too.

3.) There is no support in discussion forums from the lecturers of this course. I have seen many questions remain unanswered for many months. This is a very big drawback.

4.) There is a huge gap between what is being taught in videos and what is being asked in assignments. We can understand this by the following corollary: In the video tutorial one teacher is showing that 1 + 2 = 3. In the assignment, students are being asked to find the roots of a quadratic equation.

5.) Some questions and even their answers too technical to be understood by many students. The attempt to explain after the completion of assignment is also too technical. There should be an attempt to dive deeper to help weaker students. If time is the constraint, then make another basic course and let that be a prerequisite of this course. But please, do not mention in the introduction of this course that there is no prerequisite.

By eklektek

•Jul 25, 2020

The course seemed rather lazy using classical presentation methods not going the extra mile and benefitting from more model methods of visualisation and interaction. Instead the student has to hear a lot of words and try decipher the language and sketches of the speaker. I'm a native english speaker and I had problems. Complex subjects need a language that everybody can understand - visualisation.

There was finally some interactive visuals, in the fifth and final week, but these seemed more of an after thought. Also they were not integrated into the course. They would have yielded greater benefit if the lecturer used them too and pointed out specific points. Instead this information came from a few lines of explanatory text.

Generally the course material seemed like the minimum they could get away with, almost as if coursera charges hosting space.

In conclusion, the course has been beneficial, but it could have been so much more beneficial. So next I will look for a course more tightly coupled to my learning style and requirements. If this search fails I may return.

By Jennifer L

•Jul 5, 2020

This course was pure torture. Lessons were great and interesting but then you are testied on something entirely different! You would be wise to have some knowledge of Python before starting. Be prepared to spend days trying to pass assessments that were never explained. Oh, and there's no supporting materials to help you navigate! Just thousands of pleas from other students begging for help and guidance. Took me three months to finally complete. I would have dropped by I needed it as a pre-requisite.

By Mesum R H

•Aug 26, 2018

The course tries to cover every edge of Linear Algebra but fails to integrate each step with what relationship it has with Machine Learning. Core Formulas and Mathematical derivations are shoved down from throat without any respect for learners from non-engineering or computer science background. Other than week 1,2 rest was completely case study or example less UN-intuitive lectures of matrix formations and transformations. Needs a severe revamp with better examples and broader picture.

By Arno D

•Dec 19, 2018

Some concepts were not clearly explained and there were a lot of issues with assignment grading working properly.

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