Class Central is learner-supported. When you buy through links on our site, we may earn an affiliate commission.

The Hong Kong University of Science and Technology

Matrix Algebra for Engineers

The Hong Kong University of Science and Technology via Coursera

Overview

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

Related Courses

Reviews

4.8 rating, based on 440 reviews

Start your review of Matrix Algebra for Engineers

  • 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.
  • 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!
  • Anonymous
    Very detailed on the steps which is something that clueless students like me need. Mr Chasnov has demonstrated good teaching that requires critical thinking, which is not something easy to achieve. hopefully he I can get another class with him teaching.
  • 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
    Jeff chesnov is Amazing .

    the concepts were simply explained

    The assignments weren't large

    Some topics were explained so simply i couldn't believe they were so simple.
  • Anonymous
    Me resultó un curso muy bueno, y me completo una parte que me faltaba, aunque se, que es muchísimo lo que me falta, pero este curso me ayudo.
  • Anonymous
    This course contain lot of important point for compitative exams and engineering

    And I learnt most helpful facts from this cource

  • T N KAVITHA
    1
    INTRO TO MATRIX, DETERMINANT, RANK, INVERSE, EIGEN VALUES, VECTORS, DIAGONALISATION EVERYTHING VERY UNDERSTANDABLE. THANK YOU
  • Anonymous

    Anonymous completed this course.

    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
    It is one of the best courses that I had done in the recent past. It is very helpful with the basic concepts explained in a better and simpler way with examples. I recommend this course for beginners who have passion towards learning the fundamentals of matrix algebra. The course includes the definition of matrix, types of matrices, symmetric and non symmetric matrix. Also includes in detail the concept of eigen values and eigen vectors. With the way it is explained, I could able to complete the course in 5 days. For teachers, professional and engineering students this course is highly recommended. I am very happy that I could able to complete another course in coursera. Thank you for the opportunity to learn.
  • Profile image for Khôi Đoàn Minh
    Khôi Đoàn Minh
    I think this course is awesome, each of your lessons using concrete examples for the new definitions and do it step by step make new learner can be easily familiar with new concepts of fundamental matrix algebra. The way you demonstrate the lecture is fascinating and it attracts my interests to learn. With the exercises, they are not hard but enough to be get along with the algebra. In my opinion, the most difficult topic is about determinant and eigenvalues (hard to get it right away). At last I would like to say my thank to your useful course and hope it may help more students in the future. So see you in the next relevant course! Best regards!
  • Anonymous
    It was nice performance review is a regulated assessment in which managers assess an employee’s work performance to identify their strengths and weaknesses, offer feedback and assist with goal setting.

    The frequency and depth of the review process may vary by company based on company size and goals of the evaluations.

    This quarterly performance review example has sections for both achievements and areas of improvement. It also has a section for core values, as this must be a key performance indicator at this company. Different companies will have different measuring sticks for success.
  • Anonymous
    Thanks a lot for this this made me enough to learn something new as an engineering student of this course. I've been through a lot seems all of this will come to its place to be used someday in my future and last enough through my golden years. Wish my future children learn this so that they won't hesitate to fight along with others. Mathematics and another ideal for Engineers will be helped by this through a lot that hoping can be helpful in other as for the new features and future Engineers in this wide wide universe world to be explored.
  • Anonymous
    I've learnt so much in this course! Vector spaces and eigenvectors were rather difficult themes to learn. I still have a feeling that I can't see them in all perspectives. Some internal mechanics slips my mind. I'll need to study more learning materials describing the topics from different points of view and providing more examples. Anyway, it's a great course! And I'll come back to it to refresh my memory. Especially I liked the delivery on the video. It was real pleasure to listen to these explanations.
  • Anonymous
    THIS COURSE WAS ALSO MY SUBJECT IN MY CURRENT UNIVERSITY. HAVING THIS COURSE IN COURSERA HELPS ME A LOT TO ADVANCE MY KNOWLEDGE REGARDING THE TOPICS. IN THIS ONLINE MODULAR SYSTEM THIS IS ONE WAY TO LEARN MORE OR TO UNDERSTAND MORE ABOUT MY CURRENT SUBJECT. OTHER THAN WHAT OUR PROFESSOR TEACHING MEDIA THIS COURSE IN COURSERA WAS ALSO MY LEARNING TOOLS. I HOPE SOME STUDENT WILL ALSO HAVE THIS SET-UP BECAUSE IT WILL HELP THEM A LOT AND THEY CAN HAVE ADVANCE LEARNING ALSO.
  • Anonymous
    The course is well structured and the practice problems force you to engage in independent thinking and research. It gives you a great foundation on how to approach problems in Linear Algebra from a theoretical point of view. I learned a lot about how to think mathematical and formulate ideas and concepts in this course. I now feel a like I have a much better understanding of what matrices are and what can be done with them. I highly recommend this course!
  • Anonymous
    A great course in deed! Back to my college days, I learned this course but got little out of it.

    Here it is a really quick refresh and catch-up for what I need to know about basic linear algebra in engineering. I was impressed by the pragmatic approach for the students. No too intimidating theory but very useful methods. What I learned is:

    LU decomposition; GS process, basis, vector spaces, Eigenvalues and Eigenvectors, Diagonalization of matrix.
  • Anonymous
    Some people learn matrices in 1 semester which is around half a year, but if you need to learn about matrices quick, and if you put enough effort and study 5-7 hours a day, here you can learn everything in 1 week ! Professor Chasnov explains difficult things very simply and after lesson you can try different kind of problems (both theoretical and practical) to remember it better. If you need to learn about matrices, this course is for you!
  • Anonymous
    This course is exceptional. Mr.Chasnov is simply phenomenal at what he does and it shows. He makes the best effort at de-abstracting the information, teaching it and demonstrating it. The man is passionate and i've learned more in this course in a little more than a week than I did a whole semester in university. This course really comes to show how powerful a tool Coursera could be and I would be forever grateful that it all started here.
  • Anonymous
    A very useful online course. I learned a lot about Matrix algebra. Mr. Chasnov's lecture is fluent and clear. I am very glad to have taken this course.

Never Stop Learning!

Get personalized course recommendations, track subjects and courses with reminders, and more.

Sign up for free