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Best of All-Time Online Course

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.

Lecture notes can be downloaded from
http://www.math.ust.hk/~machas/matrix-algebra-for-engineers.pdf

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

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Reviews

4.8 rating, based on 293 reviews

Start your review of Matrix Algebra for Engineers

  • 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

    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

    Anonymous completed this course.

    Excellent course, thanks so much! Really like the fact that the videos were backed by a comprehensive set lecture notes with problems AND solutions, including some proofs. This made consuming the concepts much easier. All in all a lot to swallow in this course, but great to get acquainted again (20+ years) with this subject matter. You have an excellent manner of teaching, Jeff. Thank you!
  • Anonymous

    Anonymous completed this course.

    Professor Jeff Chasnov is a great teacher and I hope I had known his course when I first studied matrix at college. He's clear and humorous, and explains the concepts and examples really well. He is the key point that I have committed and finished this course. Thank you Professor Jeff Chasnov!
  • Anonymous

    Anonymous completed this course.

    Very nice course for engineers or to others too....all the basic concepts needed are covered...Sir is great...so if you want a course for matrix definitely go for this one...I like the screen they used much...Thats all with my end...
  • Archana Dhume completed this course.

    Course is excellent. Exercises are very good for practice and for clearing concepts.Exams covered all topics properly. Thanks for making such a wonderful course.
  • Anonymous

    Anonymous completed this course.

    This course is well-structured, well-presented, well-resourced and, as is obvious from all the reviews on Coursera and elsewhere, well-regarded. Well done, Professor Chasnov. I am choosing to award it 4 rather than 5 stars because I did find myself thinking...
  • Anonymous

    Anonymous completed this course.

    The videos made me understand all the concepts. Those
    videos are understanding and are very useful. I have learnt a lot from the course.
  • Mustafa Sadiq completed this course.

    This course is exactly what every Engineering student must take in the first or second year of their engineering career.
    Recommended to all!
  • Anonymous

    Anonymous completed this course.

    This is such a great course. I have learned a lot from Jeff's video. Thank you very much for your resources and patience in making this course!
  • 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.
  • Kais Hasan completed this course.

    very good course its really useful and i learn so much through this course , thanks for all who is help us to learn more and more .
  • Anonymous

    Anonymous completed this course.

    Quite a good course, not very complex and very useful. Everyone who wants to learn some hands-on matrix knowledge can take this course.
  • Anonymous

    Anonymous completed this course.

    HIghly recommended. Clear and concise. Just the right amount delivered in a lucid, clear style. Look out for Jeff's other courses.
  • Anonymous

    Anonymous completed this course.

    I learned a lot and understand it easier than doing it on my own. It is very helpful and convenient for us students to learn online.
  • Anonymous

    Anonymous completed this course.

    This course was really good. I was able to understand the concepts better through this course. The instructor explained well.
  • Anonymous

    Anonymous completed this course.

    The course was really informative. Sir taught the subject from the basics and made my foundations strong.
  • Profile image for Stefano Lanterna
    Stefano Lanterna
    Pros: Very nice video lectures, with good explainations. That's it. You got your 2 stars. Now to the Cons: Too few exercises. I understand that I'll not be doing those things by hand in my work life, but the exercises are SO FEW AND SIMPLE THAT YOU...
  • Katherine Blankenburg
    This was an excellent course. Instructor was very well organized and gave very clear instruction. I like the fact that when he introduced some very abstract concepts, he always tried to tie it to something concrete. The abstract concepts were a stretch...
  • Anonymous

    Anonymous completed this course.

    i enjoyed a lot with this course as wrll as with sir jaff chasnou.i m really impressed of this course and course teacher.the course were easy and applicative in the field of mathematics and engineering.assignments were from the course learned and were...

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