Online Course
Matrix Algebra for Engineers
All-Time Top 100The Hong Kong University of Science and Technology via Coursera
- 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
Class Central Tips
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
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.
-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
Class Central Charts
- #1 in Subjects / Mathematics
- #1 in Subjects / Engineering
- #1 in Subjects / Mathematics / Algebra & Geometry
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Reviews for Coursera's Matrix Algebra for Engineers Based on 68 reviews
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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!
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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.
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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!
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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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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.
videos are understanding and are very useful. I have learnt a lot from the course.
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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.
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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.
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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.
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.
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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.
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.
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Ryan
completed this course, spending 4 hours a week on it and found the course difficulty to be medium.
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!
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!
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Anonymous
Anonymous
completed this course.
This gave a well enough understanding of matrix algebra WITHOUT had having any sort of background or similar courses before. I highly recommend taking this course, especially if you are a self-learner new to matrix and linear algebra, and do not know where to start. After having taken this course, you will be independent enough to go into all the books probably scare you as a newbie. This course is absolutely stunning and I cannot stress this enough, it kind of changed a lot in my life as a self-learner and made me believe it IS possible to study this kind of material on your own. Thanks again Prof. Chasnov!
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Anonymous
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.
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
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.
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Anonymous
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.
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.
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Anonymous
Anonymous
completed this course.
This was an excellent and informative course, definitely for those interested to learn more about Matrices. The course content was challenging but manageable even for beginners. The professor explains the concepts thoroughly and provides good practice questions that test your understanding. I think doing this course has definitely put me at an advantage as I had never learnt matrix before but I am now confident in this topic.
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Anonymous
Anonymous
completed this course.
Sir your classes are well understood.. your doing a great job .. take up more classes so that we can even more cope up with you .. being grateful to be a part of this group .every question mattered me a alot and it was much more interesting as the question and assisstments were on the form .. and lucky that I choosed this course .. so I would like to appreciate your efforts and all the best sir. Thank you !!
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