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Online Course

Matrix Algebra for Engineers

All-Time Top 100

The Hong Kong University of Science and Technology via Coursera

(189)
  • Provider Coursera
  • Cost Free Online Course (Audit)
  • Session In progress
  • Language English
  • Certificate Paid Certificate Available
  • Effort 3-4 hours a week
  • Duration 4 weeks long
  • Learn more about MOOCs

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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 for Coursera's Matrix Algebra for Engineers Based on 189 reviews

  • 5 stars 83%
  • 4 stars 15%
  • 3 stars 2%
  • 2 star 0%
  • 1 star 0%

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  • 1
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
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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!
Was this review helpful to you? Yes
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.
Was this review helpful to you? Yes
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!
Was this review helpful to you? Yes
Archana D
by Archana 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.
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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!
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Mustafa S
by Mustafa 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!
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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.
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Kais H
by Kais 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 .
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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.
Was this review helpful to you? Yes
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.
Was this review helpful to you? Yes
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.
Was this review helpful to you? Yes
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.
Was this review helpful to you? Yes
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 comfortable if you took part with spirit in thus course.i am thankful to coursera and sir jaff chasnou who provided me opportunity to take this course on financial aid.really appreciable work by subject teacher.the quality of video was the best with no sound issue.i am really surprised to get such a valued course in very short time.i consider this degree as the best degree of my life.From coursera especially sir jaff chasnou i have known that the mathematics is just fun and like game,it s enjoyable.
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Anonymous
Anonymous completed this course.
nice course. very useful in study and job.

convinient for online study.

This course will introduce you to the basic elements of academic information seeking - we will explore the search process from defining a strategy to evaluating

and documenting your search results. Attending the course will make you a proficient information seeker. You will learn how to carry out comprehensive

literature searches based on your own research assignment. You will be guided through the various information seeking steps from selecting relevant search

strategies and techniques to evaluating your search results, documenting your search process and citing your sources. Attending the course will enable you to:
Was this review helpful to you? Yes
Anonymous
Anonymous completed this course.
This course helped me understand matrix algebra much better, also I truly recommend it to other students because the instructor gives example that will make the lesson easy for students to understand therefore, it will make students who wants to be an engineer think of this subject as fun because due to enrolling in this course they will be able to learn quick about the proper techniques to be used and many other more. Overall this course does not only teach students through explaining everything and giving out examples instead there are parts wherein they give chances to students to answer the following questions on their own so that they will be able to solve matrix problems on their own
Was this review helpful to you? Yes
Anonymous
Anonymous completed this course.
As someone who has been studying linear algebra independently, this is a great supplement course. There are no field axioms to learn, and vector spaces are VERY generalized. The definition of the determinant is simplified, not like one would find in Georgi E. Shilov's Linear Algebra text.

This course covers most of the important material for applications to differential equations, physics, computer science, economics, etc. Jeff Chasnov does keeps the lessons very tangible, and almost completely avoids abstraction altogether. I highly recommend the course. Even if you have taken an abstract linear algebra course, this is a good way to learn how to apply matrix algebra to real life.
Was this review helpful to you? Yes
Agung P
Agung completed this course.
Alhamdulillah. I've finished this course completely without anything problem. Thanks to Prof. Jeffrey R. Chasnov, for all materials in this course. They are very complete and easy to understanding for all participant, who enroll this course especially. Your videos are very great. I really like that, especially in the video's design.

Some things in this course that I'm very interesting in are the problem-set and quiz in end of section. I think, without them, most student can't fully understanding in this class because the material, problem-set, and quiz are a complementry whole.

Once again, thanks to you, Prof. Jeffrey R. Chasnov and team who have built this course up so well.
Was this review helpful to you? Yes
Anonymous
Anonymous completed this course.
Jeffrey R. Chasnov, teaches, step by step, how to manipulate matrices.

We see how powerful matrices can be and, sometimes, in which concrete case can they be used.

Thus, from abstraction to application, I learned fundamental concept such as eingenvectors, Subspace of matrices, Gram-Schmidt process, LU decomposition etc.

The exercises help to better understand and assimilate the lectures.

The professor teaches very clearly, enthusiastically and answer quickly to the questions.

I strongly recommend this course to people who have, at least, a high school level in mathematics and want to get a full introduction in Matrix Algebra.
Was this review helpful to you? Yes
Anonymous
Anonymous completed this course.
It's easy to understand, AT FIRST. But as I got deeper and deeper about the topics, sometimes I got left behind, so I review the videos multiple times. As time goes by, I got used to these types of situation and that helped me to feel less pressure or less dumb. It is fun to see the patterns while solving each problem, the feeling of joy when you know what you must do, but there are down-times because not every time you get the correct answer. So, I need to practice more even though the course is already finished. I must use and apply these in real life problems, it’ll make my problems a little easier to solve. Thank you.
Was this review helpful to you? Yes
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