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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

Overview

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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

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

Reviews

4.9 rating, based on 738 Class Central reviews

4.9 rating at Coursera based on 4250 ratings

Start your review of Matrix Algebra for Engineers

  • Anonymous
    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…
  • 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
  • Anonymous
    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 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
    I recently completed the "Matrix Algebra for Engineers" course on Coursera, and I found it to be an excellent resource for building a strong foundation in matrix algebra. The course provides a comprehensive and well-structured curriculum, covering…
  • Anonymous
    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…
  • Anonymous
    The website was quite helpful in enhancing my comprehension of matrices and general linear algebra ideas. It clearly explained complicated topics with its effective presentation of illustrative material. It made it easier to understand matrix operat…
  • Anonymous
    This is great, and I learned a lot about vectors and matrices. Although I still find some other topics quite tricky. This has helped me understand some of the concepts I found very complicated. All the explanations on each topic were clear, and the professor did not get me confused. In addition to the clear explanations, the professor's teaching style made the material more accessible because he broke down complex ideas into manageable steps, which helped me to understand the concepts and steps in solving them efficiently. Additionally, the inclusion of other reading resources further enhanced the depth of my understanding of the course.
  • Anonymous
    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…
  • 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…
  • Anonymous
    This "Matrix Algebra for Engineers" course on Coursera was a fantastic deep dive! The clear explanations and step-by-step 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 real-world engineering problems. Highly recommend it for anyone wanting to strengthen their foundational skills!
  • Anonymous
    It is comprehensive, the speaker is evidently knowledgeable in their field. The course makes use of various tools to help students learn such as a digitized lecture of the whole course, video lectures, practice problems that ensure mastery, and final exams per module. Each module tackles its topics in a well-organized manner providing problems inter-related to one another.
  • Anonymous
    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.
  • Anonymous
    it's good but not great or extraordinary .his way off presentation is good . we can understand things but its little dificult
  • Anonymous
    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!
  • 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
    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.
  • Anonymous
    It's an excellent course; I still need to practice and improve on my own, but the content is among the most comprehensive I've found. It's reasonably priced for all the material. I was able to grasp the basics, the methods, and the exams are challenging but practical and relatively straightforward.

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