Matrix Algebra for Engineers

The Hong Kong University of Science and Technology via Coursera

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Provider

Coursera
Pricing

Paid Course
Languages

English
Certificate

Paid Certificate Available
Duration & workload

19 hours 35 minutes
Sessions

On-Demand
Subtitles

Arabic, French, Portuguese, Italian, German, Russian, English, Spanish, Thai, Indonesian, Kazakh, Hindi, Swedish, Korean, Greek, Chinese, Ukrainian, Japanese, Polish, Dutch, Turkish, Hungarian, Bengali, Pashto, Urdu, Azerbaijani, Farsi

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Mathematics for Engineers

5.0

Overview

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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 it is recommended that students take this course after completing a university-level single variable calculus course, such as the Coursera offering Calculus for Engineers. There are no derivatives or integrals involved, but students are expected to have a basic level of mathematical maturity. Despite this, anyone interested in learning the basics of matrix algebra is welcome to join. The course consists of 38 concise lecture videos, each followed by a few problems to solve. After each major topic, there is a short practice quiz. Solutions to the problems and practice quizzes can be found in the instructor-provided lecture notes. The course spans four weeks, and at the end of each week, there is an assessed quiz. Download the lecture notes from the link https://www.math.hkust.edu.hk/~machas/matrix-algebra-for-engineers.pdf And watch the promotional video from the link https://youtu.be/IZcyZHomFQc

Syllabus

MATRICES

Matrices are rectangular arrays of numbers, symbols, or expressions, arranged in rows and columns. We define matrices and show how to add and multiply them, define some special matrices such as the identity matrix and the zero matrix, learn about the transpose and inverse of a matrix, and discuss 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, which can be used to compute the matrix inverse. We also learn how to find the LU decomposition of a matrix, and how this decomposition can be used to efficiently solve a system of linear equations with changing 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, and by row or column elimination. We also learn how to diagonalize a matrix using its eigenvalues and eigenvectors, and how this can be used to easily calculate a matrix raised to a power.

Taught by

Jeffrey R. Chasnov

Reviews

4.9 rating, based on 883 Class Central reviews

4.9 rating at Coursera based on 4663 ratings

Start your review of Matrix Algebra for Engineers

Igor Konyakhin @nns2009
9

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:)
Anonymous

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

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

Great! Here's a sample review you can I recently completed the Matrix Algebra for Engineers course on Coursera, offered by Hong Kong University of Science and Technology and taught by Prof. Jeffrey R. Chasnov. This course was well-structured, cle…

Great! Here's a sample review you can

I recently completed the Matrix Algebra for Engineers course on Coursera, offered by Hong Kong University of Science and Technology and taught by Prof. Jeffrey R. Chasnov.

This course was well-structured, clear, and practical. The instructor explained each concept in a simple and understandable way, using short video lectures and step-by-step examples.

What I liked most:

Short, clear videos that made it easy to follow along

Good practice problems and quizzes after each section

Strong focus on engineering applications

A great refresher for those who studied matrices before

Some prior knowledge of basic math and calculus is helpful, but not too advanced. The pace is quick, but not overwhelming.

This course gave me a strong foundation in:

Matrix operations

Solving systems of linear equations

Vector spaces and basis

Eigenvalues and eigenvectors

⭐ Final Rating: ★★★★★ (5/5)

Highly recommended for engineering students or anyone who wants to understand matrix algebra for real-world applications.

Thank you, Coursera and HKUST!

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Anonymous

Before I took this course, I had a really difficult time with linear algebra. I could understand some of the basic concepts like the determinants and the reduced row echelon form, but while I knew other concepts such as span, nullity, and rank, I never understood them. I really liked this course because it really helped me understand them and how to apply them. It is not perfect, of course, it can be boring at times and I wish there was a provided explanation for the practice problems to know if we are right, but all in all it was a great learning experience.
Anonymous

The Matrix Algebra for Engineers course by The Hong Kong University of Science and Technology via Coursera is challenging but very worthwhile. The lessons are clear and structured, and they explain important matrix concepts used in engineering and mathematics. Some topics can be difficult and require extra practice, but the course helps build a strong understanding of linear algebra and problem-solving skills. Overall, it is a good course for students who want to deepen their knowledge of matrices and their applications.
Anonymous

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Ryan Lam @RyanLam
74

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 provides an exceptionally clear introduction to linear algebra. Professor Jeffrey Chasnov's teaching style is engaging and mathematically rigorous without being overwhelming. The focus on applications, such as the Gram-Schmidt process and LU decomposition, makes the abstract concepts feel tangible for engineering students. The quizzes are well-designed to test conceptual understanding rather than just rote calculation. Highly recommended for anyone needing a solid mathematical foundation for higher-level engineering courses.
Anonymous

This course is very good and easy. I think this course will help teachers who teach big classes. The lessons are simple and not hard to understand.
There are many examples and tasks. It is helping to explain topics better for students. Sometimes it was little difficult, but mostly it was clear. I like that the course give practical ideas for lesson.
The materials are useful and interesting. Teachers can use this in real class. I recommend this course because it help to improve teaching and save time for preparing lessons in High school.
Anonymous

This course is very good and easy. I think this course will help teachers who teach big classes. The lessons are simple and not hard to understand. There are many examples and tasks. It is helping to explain topics better for students. Sometimes it was little difficult, but mostly it was clear. I like that the course give practical ideas for lesson. The materials are useful and interesting. Teachers can use this in real class. I recommend this course because it help to improve teaching and save time for preparing lessons.
Anonymous

J’ai globalement beaucoup apprécié ce cours, qui est clair, bien structuré et très intéressant pour comprendre l’algèbre matricielle. Les explications sont de qualité et les exercices utiles, mais le temps pour réaliser les tâches demandées était parfois un peu court, ce qui pouvait rendre le rythme assez intense. Malgré cela, l’expérience reste très positive.
Anonymous

Very detailed explanation, and I have learned a lot about matrices. I would really recommend this to those who have a subject related to this topic because he explains it very well.
Anonymous

I think that this course helped me understand more of the subject than I ever could just from research or anything that a professor can say, it is also pretty detailed to how it is explained and also how the assessments are enough to keep you active in the learning process
Anonymous

Great course to learn about matrices. The concepts were tackled well with easy to follow videos. I also liked the additional readings and examples given in the course
Anonymous

The Professor's Style: Professor Chasnov is known for being incredibly clear, concise, and using a "pen and paper" style that is easy to follow.

Practicality: The focus isn't just on proofs, but on how an engineer uses these matrices to solve differential equations or fit data.

Difficulty: The transition from Row Reduction (the first half) to Eigendecomposition (the second half) is usually where the "conceptual leap" happens.
Ken Byrne @kennbyrne
1

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
Anonymous

"This course is excellent, rich in content, and easy to understand. I learned a lot of new knowledge and was able to apply it immediately to my work. The teacher's teaching methods were engaging and kept me highly interested in learning. Highly recommended for anyone looking to improve their skills! Thank you to the teacher for their hard work! This was an unforgettable learning experience that exceeded my expectations. I will recommend this platform and this course to my friends, hoping they can also benefit from it. The course design is very user-friendly, with reasonable chapter arrangements and moderate pacing."