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# Matrix Algebra for Engineers

## 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.

http://www.math.ust.hk/~machas/matrix-algebra-for-engineers.pdf

Watch the promotional video:
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
• 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

## Reviews

4.8 rating, based on 418 reviews

Start your review of Matrix Algebra for Engineers

• Anonymous
Very detailed on the steps which is something that clueless students like me need. Mr Chasnov has demonstrated good teaching that requires critical thinking, which is not something easy to achieve. hopefully he I can get another class with him teaching.
• 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
Me resultó un curso muy bueno, y me completo una parte que me faltaba, aunque se, que es muchísimo lo que me falta, pero este curso me ayudo.
• Anonymous
This course contain lot of important point for compitative exams and engineering

And I learnt most helpful facts from this cource

• T N KAVITHA
INTRO TO MATRIX, DETERMINANT, RANK, INVERSE, EIGEN VALUES, VECTORS, DIAGONALISATION EVERYTHING VERY UNDERSTANDABLE. THANK YOU
• 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
It is one of the best courses that I had done in the recent past. It is very helpful with the basic concepts explained in a better and simpler way with examples. I recommend this course for beginners who have passion towards learning the fundamentals of matrix algebra. The course includes the definition of matrix, types of matrices, symmetric and non symmetric matrix. Also includes in detail the concept of eigen values and eigen vectors. With the way it is explained, I could able to complete the course in 5 days. For teachers, professional and engineering students this course is highly recommended. I am very happy that I could able to complete another course in coursera. Thank you for the opportunity to learn.
• Khôi Đoàn Minh
I think this course is awesome, each of your lessons using concrete examples for the new definitions and do it step by step make new learner can be easily familiar with new concepts of fundamental matrix algebra. The way you demonstrate the lecture is fascinating and it attracts my interests to learn. With the exercises, they are not hard but enough to be get along with the algebra. In my opinion, the most difficult topic is about determinant and eigenvalues (hard to get it right away). At last I would like to say my thank to your useful course and hope it may help more students in the future. So see you in the next relevant course! Best regards!
• Anonymous
It was nice performance review is a regulated assessment in which managers assess an employee’s work performance to identify their strengths and weaknesses, offer feedback and assist with goal setting.

The frequency and depth of the review process may vary by company based on company size and goals of the evaluations.

This quarterly performance review example has sections for both achievements and areas of improvement. It also has a section for core values, as this must be a key performance indicator at this company. Different companies will have different measuring sticks for success.
• Anonymous
This fantastic course guides you through some of the most important topics in this field of Matrix Algebra. Each unit consists of series of short lectures and "Reading" questions that test your knowledge of that topics. The course is provided with a nice online textbook. The unit peppered with practice quizzes with which you can test your knowledge right there. At the end of each unit, there is a Quiz section that tests the overall topics covered in the unit. The gradual style, practice tests + Quiz, helped me go through the course. I highly recommend this course.
• Anonymous
Thanks a lot for this this made me enough to learn something new as an engineering student of this course. I've been through a lot seems all of this will come to its place to be used someday in my future and last enough through my golden years. Wish my future children learn this so that they won't hesitate to fight along with others. Mathematics and another ideal for Engineers will be helped by this through a lot that hoping can be helpful in other as for the new features and future Engineers in this wide wide universe world to be explored.
• Anonymous
I've learnt so much in this course! Vector spaces and eigenvectors were rather difficult themes to learn. I still have a feeling that I can't see them in all perspectives. Some internal mechanics slips my mind. I'll need to study more learning materials describing the topics from different points of view and providing more examples. Anyway, it's a great course! And I'll come back to it to refresh my memory. Especially I liked the delivery on the video. It was real pleasure to listen to these explanations.
• Anonymous
THIS COURSE WAS ALSO MY SUBJECT IN MY CURRENT UNIVERSITY. HAVING THIS COURSE IN COURSERA HELPS ME A LOT TO ADVANCE MY KNOWLEDGE REGARDING THE TOPICS. IN THIS ONLINE MODULAR SYSTEM THIS IS ONE WAY TO LEARN MORE OR TO UNDERSTAND MORE ABOUT MY CURRENT SUBJECT. OTHER THAN WHAT OUR PROFESSOR TEACHING MEDIA THIS COURSE IN COURSERA WAS ALSO MY LEARNING TOOLS. I HOPE SOME STUDENT WILL ALSO HAVE THIS SET-UP BECAUSE IT WILL HELP THEM A LOT AND THEY CAN HAVE ADVANCE LEARNING ALSO.
• Anonymous
The course is well structured and the practice problems force you to engage in independent thinking and research. It gives you a great foundation on how to approach problems in Linear Algebra from a theoretical point of view. I learned a lot about how to think mathematical and formulate ideas and concepts in this course. I now feel a like I have a much better understanding of what matrices are and what can be done with them. I highly recommend this course!
• Anonymous
A great course in deed! Back to my college days, I learned this course but got little out of it.

Here it is a really quick refresh and catch-up for what I need to know about basic linear algebra in engineering. I was impressed by the pragmatic approach for the students. No too intimidating theory but very useful methods. What I learned is:

LU decomposition; GS process, basis, vector spaces, Eigenvalues and Eigenvectors, Diagonalization of matrix.
• 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
Some people learn matrices in 1 semester which is around half a year, but if you need to learn about matrices quick, and if you put enough effort and study 5-7 hours a day, here you can learn everything in 1 week ! Professor Chasnov explains difficult things very simply and after lesson you can try different kind of problems (both theoretical and practical) to remember it better. If you need to learn about matrices, this course is for you!
• Anonymous
This course is exceptional. Mr.Chasnov is simply phenomenal at what he does and it shows. He makes the best effort at de-abstracting the information, teaching it and demonstrating it. The man is passionate and i've learned more in this course in a little more than a week than I did a whole semester in university. This course really comes to show how powerful a tool Coursera could be and I would be forever grateful that it all started here.
• Tales Dias
It is a great course for understanding the basics of Matrix Algebra. It's nice how the professor uses the light board, and the exercises in the pdf help to better understand the ideas.
But vector spaces (Null, column left...) is a confusing topic, maybe with more application examples, i would better understand it.
And I've loved the professor enthusiasm while talking about matrices and some other properties, makes me smile :- )
• 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.

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