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The Hong Kong University of Science and Technology

Matrix Algebra for Engineers

The Hong Kong University of Science and Technology via Coursera


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 it is recommended that students take this course after completing a university-level single variable calculus course. There are no derivatives or integrals involved, but students are expected to have a basic level of mathematical maturity. Despite this, anyone interested in learning the basics of matrix algebra is welcome to join.

The course consists of 38 concise lecture videos, each followed by a few problems to solve. After each major topic, there is a short practice quiz. Solutions to the problems and practice quizzes can be found in the instructor-provided lecture notes. The course spans four weeks, and at the end of each week, there is an assessed quiz.

Download the lecture notes from the link

And watch the promotional video from the link


    • Matrices are rectangular arrays of numbers, symbols, or expressions, arranged in rows and columns. We define matrices and show how to add and multiply them, define some special matrices such as the identity matrix and the zero matrix, learn about the transpose and inverse of a matrix, and discuss orthogonal and permutation matrices.
    • 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, which can be used to compute the matrix inverse. We also learn how to find the LU decomposition of a matrix, and how this decomposition can be used to efficiently solve a system of linear equations with changing right-hand sides.
    • 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.
    • 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, and by row or column elimination. We also learn how to diagonalize a matrix using its eigenvalues and eigenvectors, and how this can be used to easily calculate a matrix raised to a power.

Taught by

Jeffrey R. Chasnov


4.9 rating, based on 679 Class Central reviews

4.9 rating at Coursera based on 4107 ratings

Start your review of Matrix Algebra for Engineers

  • 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:)
  • 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!
  • 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
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  • Anonymous
    Курс өте жақсы. Тақырыптарды оңай әрі тез үйрене алдым. Бұл курсты оқу барысында матрицалар, оларға амалдар қолдану, векторлар, векторлық кеңістіктер, Грам-Шмид процесі, анықтауыштар, олардың қасиеттерін, Лаплас формуласы мен Лейбниц формулаларын үйрене алдым. Әрі әр тақырыпқа қызықты есептер шығарып, білімімді тексеретін тесттер орындадым. Барлығы маған бұл курсты толық меңгеруіме көп көмек етті.
  • Anonymous
    I highly recommend the Coursera course 'Matrix Algebra for Engineers
    '(The Hong Kong University of Science and Technology). The content is comprehensive and well-structured, with clear explanations and examples. The interactive quizzes and assignments allowed me to practice and apply the concepts learned. Overall, a valuable resource for anyone seeking to improve their algebra skills in an engineering context."
  • Anonymous
    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
    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 t…
  • Anahita Sharma
    Studying engineering, and wanted to brush up on some concepts regarding matrix algebra. Definitely learnt a lot, this course is good- concise explanations and plenty of examples too, The course pattern was easy to follow even with college classes, I could take out time to complete it in a month.
    The divisions into weeks help, and another good feature is That the instructor summarises a video at the end of each video, which makes stuff easier to put together in my mind.
  • 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
    The explanations of all topics from first principles were very informative and made subsequent sequential aspects of the course very meaningful. In my opinion, this so far is the best course on linear algebra on this platform. Other courses are good, but Professor Chasnov teaches the course at a pace that shows his interest in letting students understand every bit of what he says. I am glad I took the course.
  • Anonymous
    The course did not make use of Python libraries designed specifically to solve linear algebra problems. I believe the goal was to teach the student not to rely on libraries when coding. I believe that, in theory, a person should be able to write code without the use of libraries, and that this was perhaps one of the goals of this course. but overall this has taught me a lot about matrices
  • Anonymous
    Such a great course, with interesting applications and intuitive explanations! I actually had studied the covered topics before, but this course solidified my understanding with great applicable examples. Hence, I cannot say it will be an easy course for everyone who takes it considering someone that isn't familiar with the core intuition behind matrix algebra.
  • Тангиркул Мухаммед Жандарбекович
    I highly recommend the Coursera course 'Matrix Algebra for Engineers.The content is comprehensive and well-structured, with clear explanations and examples. The interactive quizzes and assignments allowed me to practice and apply the concepts learned. Overall, a valuable resource for anyone seeking to improve their algebra skills in an engineering context."
  • Anonymous
    In my opinion, it is a very complete course, also very well explained.
    It does not receive 5 stars from me because it does not have some more things that students from computer engineering careers, like me study at university, like Jordan, Gershgorin, and some others, but it has the most important themes so it is excellent.
  • Anonymous
    I am very grateful to you for this course, at my university, at first it seemed to me difficult to exclude Gauss, but after this course it seems something obvious and easy. I liked the 2nd week the most, there were very interesting topics and methods.Finally, thank you again for your work, Professor.
  • Anonymous
    Jeffrey Chasnov is a very charismatic fellow and an outstanding instructor. Lessons were very concise and clutter free. He made a great effort of bringing us engineers (some in formation, some brushing up concepts) the best possible approach for the topics explored. The companion book (the electronic document provided) is the best supplementary material I’ve come across for a MOOC. When someone cares, it shows. It truly shows.
  • Anonymous
    Good building of fundamentals in an easy to understand way. Weeks 3 and 4 were especially interesting as they covered the applications of matrix algebra on actual problems, and not just solving equations or getting the transpose.

    Overall a very educational and interesting course.
  • Anonymous
    This linear algebra course is very well organized and presented by Dr. Chasnov. I enjoy learning Linear Algebra from this instructor as he explains the concepts really well. I only wish they have more practice problems and a few more topics.
  • Anonymous
    Great teacher and great content. Many exercises from all levels. Prof. Chasnov is a great communicator and the content and pace of the videos are just right. There are challenging exercises but also push us to do better and think analytrically.

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