Matrix Algebra for Engineers
The Hong Kong University of Science and Technology via Coursera

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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 it is recommended that students take this course after completing a universitylevel 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 instructorprovided 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
https://www.math.hkust.edu.hk/~machas/matrixalgebraforengineers.pdf
And watch the promotional video from the link
https://youtu.be/IZcyZHomFQc
Syllabus
 MATRICES
 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.
 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, 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 righthand 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 GramSchmidt process, orthogonal projection, and the matrix formulation of the leastsquares 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, 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
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Reviews
4.9 rating, based on 753 Class Central reviews
4.9 rating at Coursera based on 4311 ratings
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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 indepth and with more topics covered such as SVD decomposition and others:) 
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

I recently completed a Matrix course on Coursera, and the experience was truly enriching. The course, structured with clarity and precision, adeptly navigated through the intricate world of matrices, offering a comprehensive understanding of their…

Мен инженерлерге арналған матрица курсын оқу барысында өзіме көптеген жаңа білімдер мен пайда ала алдым. Курсты қалаған уақытымда өзіме ыңғайлы орындар да жақсы әрі сапалы оқи алдым. Жаңа сапалы білім үшін профессорлар мен лекторларға алғыс айтамын.

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 wellprepared 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 mustknow for all of you.
Thank you Professor Chasnov for this amazing course! 
I recently completed the "Matrix Algebra for Engineers" course offered by The Hong Kong University of Science and Technology via Coursera, and it was an exceptional learning experience. The course content was meticulously structured, providing a sol…

Covers all fundamental topics pertaining matrix algebra, with a clear and concise approach to each topic. A perfect course for everyone as it begins with the very basics providing a solid foundation for the subject and works its way up to complex to…

An excellent teacher for an outstanding course, you have truly made a remarkable impact with your expertise and dedication. To further enrich the learning experience, it would be highly beneficial to incorporate the concept of linear transformations…

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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

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 selfmotivated learning will be required t…

This "Matrix Algebra for Engineers" course on Coursera was a fantastic deep dive! The clear explanations and stepbystep examples made grasping complex concepts like vector spaces and eigenvalues a breeze. The assignments were challenging but rewarding, solidifying my understanding of how matrix algebra applies to realworld engineering problems. Highly recommend it for anyone wanting to strengthen their foundational skills!

Сәлеметсіздер ме! Маған курс ұнады, не дегенменде кемшіліктер болды әсіресе материалды аудару жағынан және дыбыстамада да бірқатар кемшіліктер болды. Сіздерді осы тұстарыңызды жөндейді деген ойдамын.

"Matrix Algebra for Engineers" course on Coursera is an excellent educational resource that effectively combines theoretical knowledge with practical applications. It is wellsuited for engineers, students, and anyone looking to enhance their understanding of matrix algebra. I highly recommend this course to anyone interested in mastering this essential mathematical tool.

it's good but not great or extraordinary .his way off presentation is good . we can understand things but its little dificult

Курс маған қатты ұнады, әр сабақтың соңындағы тапсырмаларыда күшті есте қалардай болды ең бастысы бұл курс арқылы мен сызықтық алгебра курсын кеңейтілінген деңгейде үйреніп шықтым. Рахмет!

The Matrix Algebra course under Professor Jef Chasnav was a rewarding academic journey characterized by excellent pedagogy, rich content, and invaluable practical insights. I would highly recommend this course to anyone seeking a robust foundation in matrix algebra, whether for academic pursuits or professional development.

This Course (Matrix Algebra for Engineers) is of great value. It is well designed with excellent course contents and nicely explained by the faculty member. I really liked and enjoyed this course. Thanks Hong Kong University of Science and Technology and thanks Coursera for formulating such a course.

I highly recommend the Coursera course 'Matrix Algebra for Engineers
'(The Hong Kong University of Science and Technology). The content is comprehensive and wellstructured, 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." 
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.