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
https://www.math.hkust.edu.hk/~machas/matrix-algebra-for-engineers.pdf
And watch the promotional video from the link
https://youtu.be/IZcyZHomFQc
Overview
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 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, 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
4.8 rating, based on 767 Class Central reviews
4.9 rating at Coursera based on 4432 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 in-depth 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
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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…
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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! -
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…
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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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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.
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The Matrix Algebra course on Coursera offers a solid introduction to key concepts like matrix operations, determinants, eigenvalues, and their applications in data science. The instructor presents material clearly with engaging visuals, and the course includes interactive quizzes and hands-on assignments. It’s accessible for beginners and those refreshing their knowledge, supported by active discussion forums. Overall, it’s a highly recommended course for building a foundational understanding of matrix algebra, particularly for its applications in machine learning.
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Well, when the sun goes down and the moon comes up I turn into a teenage Goo Goo Muck Yeah, I cruise through the city and I roam the streets Looking for something that is nice to eat, mmm You better duck When I show up The Goo Goo Muck I'm the night…
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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
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"Matrix Algebra for Engineers" course on Coursera is an excellent educational resource that effectively combines theoretical knowledge with practical applications. It is well-suited 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.
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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.
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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." -
"Matrix Algebra for Engineers is exceptionally well-structured and highly informative, providing clear explanations and practical examples. The course breaks down complex concepts into digestible segments, making it easy to follow and ideal for engineers looking to master matrix algebra fundamentals."
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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.
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"Matrix Algebra for Engineers by HKUST on Coursera is a comprehensive and well-structured course that offers clear explanations of complex concepts. It's perfect for anyone looking to strengthen their understanding of matrix operations and their applications in engineering."
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This course is a breakdown of complex methods in the algebra of matrices, I can say this as a mathematics graduate that this course will help you in understanding the core of matrix algebra, it covers almost all of what you need to know in order to use matrices
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Matrix Algebra for Engineers helped me remember some notions I had learnt when I was in high school and gave me an in-depth teaching of calculations that I barely knew. I do recommend every person interested in dealing with matrices in depth to take this course.
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The way the topics are explained is clear. The concepts and theory is presented in a very approachable way and then is understood much better with the examples and exercises. The quizzes are essential when appropriating all the knowledge you have adquired.
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The course is amazing. It's surprisingly easy to understand. It reminds me of when I was still in my undergraduate taking Linear Algebra Class, trying to understand a difficult concept. Each video explains a core subject without taking a bush.
