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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

4.9 rating, based on 571 Class Central reviews

4.9 rating at Coursera based on 3628 ratings

Start your review of Matrix Algebra for Engineers

• The course is great!

I studied linear algebra before, so I used this course as a refresher. All explanations were concise and clear. Instructor doesn't prove everything, but it's a good exercise to pause and prove the remaining parts yourself. Speech is somewhat slow so I watched videos at 1.75x speed (but again, I was familiar with linear algebra, so this speed was comfortable for me). I just wish it would be longer, more in-depth and with more topics covered such as SVD decomposition and others:)
• Found this course to be excellent in covering matrix algebra. Covered the areas of concern for engineering from introduction to matrices to LU decomposition. It gets harder as the topics are covered with gaussian and reduced row echelon a foundation up to eigenvalues and eigenvectors. Explained well and enjoyed
• Ryan Lam 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!
• Anonymous
This course was great in terms of learning the mechanics for solving linear algebra problems. After completing the course, I feel like I have a better understanding of linear algebra but also that much more self-motivated learning will be required to...
• Anonymous
Este curso es un breve resumen de lo que es la clase de algebra lineal, el material brindado por este curso de mucha ayuda, ya que, apoya a los estudiantes a comprender de una manera mas clara los diferentes tópicos que se verán a lo largo de la clase. Este curso me fue muy útil ya que con los videos y lecturas, pude reforzar los conocimientos de la clase, de hecho aprendí nuevas formas de como visualizar los conceptos y ejercicios para resolverlos de una manera mas practica y rápida. Es un curso que recomendaría, ya que, los métodos de enseñanza en este curso son muy efectivos y de mucho provecho.
• Anonymous
Un excelente curso, es de mucho provecho pues nos ayuda a reforzar conocimientos que veremos en nuestras clases de la facultad de ingeniería, cosas que utilizaremos en nuestras futuras clases, o que ya hemos visto y se nos ha olvidado, además de que muy entretenido el hacer cada actividad, ir sumando minutos como ir sumando puntos, y con la ventaja de poder retroceder un video en caso que no hayamos entendido, no nos haya quedado claro un punto, y el profesor es una persona brillante en el área, explica excelente, entendible a pesar de que algunas cosas eran muy complejas, en conclusión, un curso demasiado excelente, se merece mucho las 5 estrellas, muchas gracias por tomarse el tiempo de hacerlo para que nosotros ´pudiéramos recibirlo.
• Anonymous
This is a quick introduction to matrix algebra. I have learned linear algebra before, and I am familiar with dirac notion in quantum mechanics, but I still learn new things from this course. For example, the relation among null space, colomn space, row space, left null space. Besides, the application in the linear regression impressed me a lot. I learned to understand linear regression as minimizing cost function or maximize likelihood and this course provides a new aspect of understanding linear regression. Last but not least, there is accompanied course note and instructor is accessible and open for your questions about course contents. Cannot wait to learn the next course in the series!
• Ken Byrne
This course takes a user through matrix algebra in a systematic route, covering matrices their definition, addition, multiplication and special types of matrices. How to transpose a matrix, Inverse, etc. It then goes into linear equations with gaussian elimination and reduced row echelon and LU decomposition, before going into vector spaces the eigenvalues and eigenvectors...Lost, then you really need to take this course to truly understand these areas of algebra. It is presented in a clear ,concise and excellent format than will back up any class you missed or couldn't understand before. excellent number of weeks o this very important subject for engineers
• Nguyen Quan
Thanks professor J. R. Chasnov for amazing course, I have learned a lot from it.
I am interested most in part 4 (the determinants, eigenvalues and matrix powers) because the knowledge is easy to digest.
I find the most challenging is part 3 (vector space and 4 subspaces) because the definition is kind of abstract.
Moreover, I think it would be more interesting if you can include some practical application for each part so students can easily remember (like the Gaussian elimination).
I hope to join more classes from you in the future.
• Anonymous
The course was informative and provided in one of the most simplified ways without reducing the importance of the topic. I have learned a lot in this course.
I was somehow confused about the column and rows vector spaces. I was waiting for that information (the row vector space is the same even you take vectors from matrix A or its RREF but the column space is not). Finally, I have to say that this course was inspiring and well-presented.
Thank you for this well-prepared course
• Anonymous
I studied linear algebra before, so I used this course as a refresher. All explanations were concise and clear. Instructor doesn't prove everything, but it's a good exercise to pause and prove the remaining parts yourself. Speech is somewhat slow so I watched videos at 1.75x speed (but again, I was familiar with linear algebra, so this speed was comfortable for me). I just wish it would be longer, more in-depth and with more topics covered such as SVD decomposition and others:)
• 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
Yes this is an amazing course, So amazing that it is very amazing! I want this course to be more amazing to the next coming amazing students. THere is no need to change something in this amazing course because the course is already amazing on it's own amazing way! Thank you for teaching us amazing things with matrixes for civil engineers and it will be an awsome and amazing experience and very amazingly useful in my amazing career
• Anonymous
Jeff chesnov is Amazing .

the concepts were simply explained

The assignments weren't large

Some topics were explained so simply i couldn't believe they were so simple.
• Anonymous
I learnt about various properties and types of matrices and how we solve them using gaussian elimination, reduced row echelon form, LU decomposition and various others. I have also learnt about the four fundamental subspaces of a matrix, the Gram-Schmidt process, orthogonal projection, and the matrix formulation of the least-squares problem, which I was having limited knowledge of. Overall this was a great course.
• Anonymous
This course is very helpful to engineering students. It lets you grasp on the concepts on the topics/lessons that most engineering students will tackle in the future. The lessons taught in this course serve as foundations for students like me. I appreciate spending my time on this course because I was able to understand all of the lessons because of the professionalism displayed by the lecturer.
• Anonymous
I learned well because the discussion by Prof. Chaznov was delivered in a smooth, clear, and calm manner which really helped me understand the topics. With this coursera course, I learned matrix algebra from a different angle and was able to apply it to the teachings of my professor. I learned and I enjoyed while learning. The most important part for me is that I enjoyed the course, so thank you,
• Anonymous
Is a quite new teaching method to me, watching videos on a teaching platform, we can adjust the speed of learning and can repeat watching until I understand. Everything is clear to follow. Exercises right after each session provided us a great chance the know weather I really understand the content or not. If I am not able to finish the exercise I can refer back to the previous video.
• Anonymous
Informative video lectures, challenging quizzes, and complete with reading material. Before enrolling to this course, I have no initial knowledge on matrices and with this course, I was given a chance to learn and enhance my skills in linear algebra and solve system of algebra. I learned so much in this course and will highly recommend it to my friends and classmates.
• Snehangshu Roy
One of the best introduction of applied linear algebra through matrix approach. The instructor provided all notes of lectures in pdf, which included practice problems with solutions after each lecture. The best part is there is a audit quiz at the end of of each week and the audit quiz is same as the graded quiz so one can judge his/her understanding gain from the course.

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