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Online Course

Matrix Algebra for Engineers

All-Time Top 100

The Hong Kong University of Science and Technology via Coursera

2.8k
  • 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. We define matrices and how to add and multiply them, and introduce some special types of matrices. We describe the Gaussian elimination algorithm used to solve systems of linear equations and the corresponding LU decomposition of a matrix. We explain the concept of vector spaces and define the main vocabulary of linear algebra. We develop the theory of determinants and use it to solve the eigenvalue problem.

After each video, there are problems to solve and I have tried to choose problems that exemplify the main idea of the lecture. I try to give enough problems for students to solidify their understanding of the material, but not so many that students feel overwhelmed. I do encourage students to attempt the given problems, but if they get stuck, full solutions can be found in my lecture notes.

The mathematics in this matrix algebra course is presented at the level of an advanced high school student, but typically students would take this course after completing a university-level single variable calculus course. There are no derivatives or integrals in this course, but student's are expected to have a certain level of mathematical maturity. Nevertheless, anyone who wants to learn the basics of matrix algebra is welcome to join.

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

Watch the course overview video at
https://youtu.be/IZcyZHomFQc

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
-We learn about determinants and the eigenvalue problem. We learn how to compute determinants using a Laplace expansion, the Leibniz formula, or by row or column elimination. We formulate the eigenvalue problem and learn how to find the eigenvalues and eigenvectors of a matrix. We 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 53 reviews

  • 5 stars 87%
  • 4 stars 13%
  • 3 star 0%
  • 2 star 0%
  • 1 star 0%

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  • 1
Anonymous
a year ago
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
Was this review helpful to you? Yes
Anonymous
12 months ago
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
6 months ago
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
a year ago
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
a year ago
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.
Was this review helpful to you? Yes
Mustafa S
12 months ago
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!
Was this review helpful to you? Yes
Anonymous
a year ago
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.
Was this review helpful to you? Yes
Anonymous
5 months ago
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!
Was this review helpful to you? Yes
Anonymous
a year ago
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
Kais H
a year ago
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 .
Was this review helpful to you? Yes
Anonymous
12 months ago
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
5 months ago
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
Anonymous
5 months ago
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
7 months ago
Anonymous completed this course.
The course was very well presented in three ways.

The first, the educator was very clear and the presentation technique through the use of a window board was

excellent. The educator's hands on approach through exposition and examples is to be commended.

The second the material is presented in a fashion that was not simple but not too hard to grasp given

effort. The reinforcement through the use of quizzes, with solved examples, and examination though

the use of tests, without solved examples, works.

The Third, the excellent text accompanying the course is first class.

This is a high quality course.
Was this review helpful to you? Yes
Anonymous
10 months ago
Anonymous completed this course.
The course understood the needs of science and engineering subject, focus on the necessary part of the theory and skills that is necessary to understand the professions knowledge and literature and presents them in a very clear manner, which is something important that some maths courses trends to forget. The emphasis on the usefulness of matrix actually help different area to think in a clearer way specially the vector space concepts and this actually help students to appreciate the beauty of such theory and will be more willing to learn more harassing maths.
Was this review helpful to you? Yes
Anonymous
2 months ago
Anonymous completed this course.
I completed and have cert. This course is very well organized. The course encourage me to go further in Phyasics for my life-long study. And expect course about 'vectors and tensors'

During I taking this course I built study site in Korean.

http://math-mass-goodkook.blogspot.com/search/label/%EC%9D%B4%EA%B3%BC%EC%83%9D%EC%9D%84+%EC%9C%84%ED%95%9C+%ED%96%89%EB%A0%AC+%EB%8C%80%EC%88%98

Thanks Prof. Chasnov for providing great course.

Was this review helpful to you? Yes
Duc T
10 months ago
by Duc completed this course, spending 4 hours a week on it and found the course difficulty to be medium.
This was an interesting course, and I learned a lot about matrix algebra. I also took another course of him, which is Fibonacci Numbers and the Golden Ratio. This is the second course of professor Jeffrey Chasnov that I took, and I really like both of his courses. I hope that professor Jeffrey Chasnov will create some more interesting math courses in the future.
Was this review helpful to you? Yes
Adam C
8 months ago
Adam completed this course, spending 8 hours a week on it and found the course difficulty to be medium.
This is a really good course about Matrix Algebra, there are exercises for particular lectures which really help understand concepts. The quality of videos is high and there are no mistakes in quizzes. I really appreciated it. I would not mind if the course was a bit longer but well everything good ends too quickly.
Was this review helpful to you? Yes
Anonymous
7 months ago
Anonymous completed this course.
It was a wonderful refresher of my fundamentals of Vector Algebra. The course is very well designed for online learning. The instructor is very knowledgeable, clear and concise. I would highly recommend the course for all learners - both new and advanced with interest in Mathematical fundamentals underlying Engineering.
Was this review helpful to you? Yes
Anonymous
7 months ago
Anonymous is taking this course right now.
Taking this course is paramount important as it is going to enable me to counter some other hard courses such as Physics and Statistics in the near future.It is also going to be an instrumental in pushing me ahead and help me deal with my careers like Geology,Mathematics,Physics and Statistics.
Was this review helpful to you? Yes
  • 1

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