Matrix Algebra for Engineers

The Hong Kong University of Science and Technology via Coursera

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Details

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Provider

Coursera
Pricing

Free Online Course (Audit)
Languages

English
Certificate

Paid Certificate Available
Duration & workload

4 weeks long, 20 hours worth of material
Sessions
Level

Beginner
Subtitles

Arabic, French, Portuguese, Italian, German, Russian, English, Spanish

A Best Course of All Time

Found in

Part of

Mathematics for Engineers

Overview

Class Central Tips

This course is all about matrices, and concisely covers the linear algebra that an engineer should know. The mathematics in this course is presented at the level of an advanced high school student, but typically students should take this course after completing a university-level single variable calculus course. There are no derivatives or integrals in this course, but students are expected to have attained a sufficient level of mathematical maturity. Nevertheless, anyone who wants to learn the basics of matrix algebra is welcome to join.

The course contains 38 short lecture videos, with a few problems to solve after each lecture. And after each substantial topic, there is a short practice quiz. Solutions to the problems and practice quizzes can be found in instructor-provided lecture notes. There are a total of four weeks in the course, and at the end of each week there is an assessed quiz.

Download the lecture notes:
http://www.math.ust.hk/~machas/matrix-algebra-for-engineers.pdf

Watch the promotional video:
https://youtu.be/IZcyZHomFQc

Syllabus

MATRICES

Matrices are rectangular arrays of numbers or other mathematical objects. We define matrices and how to add and multiply them, discuss some special matrices such as the identity and zero matrix, learn about transposes and inverses, and define orthogonal and permutation matrices.

SYSTEMS OF LINEAR EQUATIONS

A system of linear equations can be written in matrix form, and can be solved using Gaussian elimination. We learn how to bring a matrix to reduced row echelon form, and how this can be used to compute a matrix inverse. We learn how to find the LU decomposition of a matrix, and how to use this decomposition to efficiently solve a system of linear equations with evolving right-hand sides.

VECTOR SPACES

A vector space consists of a set of vectors and a set of scalars that is closed under vector addition and scalar multiplication and that satisfies the usual rules of arithmetic. We learn some of the vocabulary and phrases of linear algebra, such as linear independence, span, basis and dimension. We learn about the four fundamental subspaces of a matrix, the Gram-Schmidt process, orthogonal projection, and the matrix formulation of the least-squares problem of drawing a straight line to fit noisy data.

EIGENVALUES AND EIGENVECTORS

An eigenvector of a matrix is a nonzero column vector that when multiplied by the matrix is only multiplied by a scalar, called the eigenvalue. We learn about the eigenvalue problem and how to use determinants to find the eigenvalues of a matrix. We learn how to compute determinants using the Laplace expansion, the Leibniz formula, or by row or column elimination. We also learn how to diagonalize a matrix using its eigenvalues and eigenvectors, and how this leads to an easy calculation of a matrix raised to a power.

Taught by

Jeffrey R. Chasnov

Charts

#2 in Subjects / Mathematics
#2 in Subjects / Engineering
#1 in Subjects / Algebra / Linear Algebra
#1 in Subjects / Mathematics / Algebra

Reviews

4.9 rating, based on 620 Class Central reviews

4.9 rating at Coursera based on 3844 ratings

Start your review of Matrix Algebra for Engineers

Igor Konyakhin @nns2009

The course is great!

I studied linear algebra before, so I used this course as a refresher. All explanations were concise and clear. Instructor doesn't prove everything, but it's a good exercise to pause and prove the remaining parts yourself. Speech is somewhat slow so I watched videos at 1.75x speed (but again, I was familiar with linear algebra, so this speed was comfortable for me). I just wish it would be longer, more in-depth and with more topics covered such as SVD decomposition and others:)
Ryan Lam @RyanLam

Ryan Lam completed this course, spending 4 hours a week on it and found the course difficulty to be medium.

I am a high school student. I took the course because I need to prepare my studies in undergraduate mathematics. Although this course is meant to be for engineers, nevertheless, it is an amazing course.

Concepts are clearly explained, and there are a lot of concrete examples. The exercises are also well-prepared in the sense that it reflects the learning outcome of the class.

I highly recommend this course to future undergraduate students who want to study science as their major, because matrix algebra and linear algebra is a must-know for all of you.

Thank you Professor Chasnov for this amazing course!
Ken Byrne @kennbyrne

Found this course to be excellent in covering matrix algebra. Covered the areas of concern for engineering from introduction to matrices to LU decomposition. It gets harder as the topics are covered with gaussian and reduced row echelon a foundation up to eigenvalues and eigenvectors. Explained well and enjoyed
Anonymous

I am a seasoned software engineer going back to school next year for studying physics. I attended this course to improve my skills in matrix algebra and spent a really good time. Many thanks to Pr. Chasnov for making this course available. Here’s what...

I am a seasoned software engineer going back to school next year for studying physics. I attended this course to improve my skills in matrix algebra and spent a really good time. Many thanks to Pr. Chasnov for making this course available.

Here’s what I liked
Having videos + a PDF is really useful. Each one left alone would be hard to work with.
Having exercises for each chapter really helps memorizing.
The video on transparent board with multiple colors is really readable. Seeing you speaking makes the experience nice and much better than most math courses on internet.
Each video ending with a recap really helps understanding.
You take time to answer questions, thank you a lot. This makes your course better than lot training I could find before. Some of your answers were a bit concise to me however (mainly in the Differential equation courses).
Letting us demonstrate facts about matrices rather than just memorizing them is great. On the other hand, I sometime felt like we are given recipes to apply that appeared to me like black magic. But I understand that proving everything would make the course much longer so I finally think you chose the best tradeoff.

My wife and I both got the music intro and outro sentence of each video saved in our mind now :D

Thank you very much and congratulation for this work Pr. Chasnov!
Anonymous

This is a game changer for me. I have passed through matrix algebra class before but this one is more in-depth and has deepen my understanding of matrix algebra. Thank you!
Anonymous

This course was great in terms of learning the mechanics for solving linear algebra problems. After completing the course, I feel like I have a better understanding of linear algebra but also that much more self-motivated learning will be required to...

This course was great in terms of learning the mechanics for solving linear algebra problems. After completing the course, I feel like I have a better understanding of linear algebra but also that much more self-motivated learning will be required to gain even better understanding.

There are several areas for improvement in the course content and also some additional things I would love to see as far as building upon this foundational course from Professor Chasnov:

1) Professors Chasnov's teaching style is excellent and the use of the lightboard is impactful. Future courses taught in this way and style would be beneficial for students.

2) Although the lecture content is great, the solutions to many of the follow-on exercises that required proofs were too condensed and didn't seem adequate with regards the rigorous steps required to prove things.

3) The flow of video content going from vectors spaces to solving the least squares problem took a big conceptual leap that wasn't easily apparent to newcomers to linear algebra. I think there needs to be one more video prior to the discussion of the least squares problem designed to fill this gap.

4) It would be great to have a follow-up course dedicated to four or five engineering and business problems and using the linear algebra tools from this course to solve those problems. This would solidify not only the concepts learned in this course but also why these concepts are critical and impactful to solving real world problems.

5) It would be great to have another follow-up course dedicated to computer coding of the content from item 4 using a language like Python.

6) Specifically, it would be great to have a course on machine learning and the critical role of linear algebra in the context of developing machine learning solution. This course would take smaller tasks within the broader machine learning solutions and demonstrate how to use linear algebra to tackle those tasks (for example PCA to perform dimensionality reduction).

Thank you for an insightful class.

Nick Jathar
Anonymous

The course covers the most important basic topics in Linear Algebra.
The lightboard Jeff uses is very convenient as a visual aid. In general, I enjoyed the course flow. I also noticed the professor is pretty active answering questions: some of his replies were quite recent (1 or 2 weeks old).
A couple of things one might find missing in the course are the geometric interpretation/behavior of matrices as well as Linear Transformations.

I definitely recommend the course for beginners/intermediate learners. Good luck with the
course and remember reviewing what you've learnt several times is key :)
Anonymous

The course was for me very helpful in learning the different topics under matrix algebra for engineers; it has helped me by learning all the lessons through video lectures that had step-by-step processes, other ways that had helped me was the practice quizzes since I was able to retake any time so that I could correct my mistakes and be able to understand how the process works. Additionally, Coursera has helped me attain the knowledge that I need to understand the topics of Matrix Algebra for Engineers since this will be a big help for me since it is one of the courses I am taking.
Nguyen Quan

Thanks professor J. R. Chasnov for amazing course, I have learned a lot from it.
I am interested most in part 4 (the determinants, eigenvalues and matrix powers) because the knowledge is easy to digest.
I find the most challenging is part 3 (vector space and 4 subspaces) because the definition is kind of abstract.
Moreover, I think it would be more interesting if you can include some practical application for each part so students can easily remember (like the Gaussian elimination).
I hope to join more classes from you in the future.
Anonymous

Este curso es un breve resumen de lo que es la clase de algebra lineal, el material brindado por este curso de mucha ayuda, ya que, apoya a los estudiantes a comprender de una manera mas clara los diferentes tópicos que se verán a lo largo de la clase. Este curso me fue muy útil ya que con los videos y lecturas, pude reforzar los conocimientos de la clase, de hecho aprendí nuevas formas de como visualizar los conceptos y ejercicios para resolverlos de una manera mas practica y rápida. Es un curso que recomendaría, ya que, los métodos de enseñanza en este curso son muy efectivos y de mucho provecho.
Anonymous

Anonymous completed this course.

Learning materials are very organized and each problem always comes with examples. Since I am taking some other courses, the volume is bit larger for me. I wish I get more pair of exercise and solution per topic and ideally this could be 6 weeks. One of highlight is to compute the least square problem (fitting something) using matrix algebra and solving eigenvalue problem. The instructor often mentions about benefit using those algorithm in terms of the efficiency & cost of computation. This is nice indication for me because I'm software engineer who often just "use" existing math libraries, and now I can imagine how they wrote them. I might write my own someday :D
Anonymous

I learnt about various properties and types of matrices and how we solve them using gaussian elimination, reduced row echelon form, LU decomposition and various others. I have also learnt about the four fundamental subspaces of a matrix, the Gram-Schmidt process, orthogonal projection, and the matrix formulation of the least-squares problem, which I was having limited knowledge of. Overall this was a great course.
Anonymous

I took advanced Math 10 years ago and needed to brush up my skills for grad school. This course was just excellent, with very clear explanations and excellent examples, I really enjoyed my time learning.

I recommend this course to anyone who doesn't know anything about matrices or linear algebra, or even if want to brush up your skills, like me, this course is amazing for all levels.
Snehangshu Roy

One of the best introduction of applied linear algebra through matrix approach. The instructor provided all notes of lectures in pdf, which included practice problems with solutions after each lecture. The best part is there is a audit quiz at the end of of each week and the audit quiz is same as the graded quiz so one can judge his/her understanding gain from the course.
Anonymous

This course on Matrix Algebra for engineers is very good. It is nicely designed starting from the fundamentals and is user oriented. We could understand the concepts of Matrix algebra and had obtained a clear understanding. The application of Matrix Algeebra is dealt with in good format. On the whole the course is very good and we had improved our knowledge on Matrix Algebra
Anonymous

This class has a very beautiful and practical topic. Professor Chasnov's mastery of the subject along with his beautiful teaching method will make you interested to. Also, the presence of numerous practical examples in this course will help you if the application of abstract mathematical concepts in your life is unclear. Many thanks to the teacher!
Anonymous

The course gives a fundamental understanding of matrices and how they are used mathematically. Professor does a great job in explaining the concepts. I like the way he writes down stuff on the lightboard to make things for clear to the students. The accompanying study material is excellent. I am sure it would serve as a reference guide for me in the future.
Anonymous

This course gives you good fundations on linear algebra. By the way in some part of the course concepts are tackled in a very abstract way and this makes it harder to grasp some of them. It is a complex course and not a piece of cake but with patient and practice you can gain a reliable idea in matrix algebra. I'd suggest it to some friends.
Anonymous

A excellent online course is interesting and difficult. It calls on pupils to take part, encourages them to contribute, and grabs their interest. It encourages students to develop their knowledge, skills, and capacities while maximizing the fun of learning. A good online course will test your cognitive abilities, and this one did exactly that.
Anonymous

At first, I thought that the online course would be too difficult for me due to its rapid pace. However, the lectures and study materials are user-friendly and manageable thus I managed to finish the course sufficiently with enough practice. I recommend others to undertake such courses since it is very efficient for students like us.