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.

# Matrix Algebra for Engineers

Offered By

## Matrix Algebra for Engineers

## About this Course

### Learner Career Outcomes

## 50%

## 50%

### What you will learn

Matrices

Systems of Linear Equations

Vector Spaces

Eigenvalues and eigenvectors

### Skills you will gain

### Learner Career Outcomes

## 50%

## 50%

#### Shareable Certificate

#### 100% online

#### Flexible deadlines

#### Beginner Level

#### Approx. 14 hours to complete

#### English

## Syllabus - What you will learn from this course

**5 hours to complete**

## 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.

**5 hours to complete**

**11 videos**

**25 readings**

**5 practice exercises**

**4 hours to complete**

## 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.

**4 hours to complete**

**7 videos**

**6 readings**

**3 practice exercises**

**5 hours to complete**

## 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.

**5 hours to complete**

**13 videos**

**14 readings**

**5 practice exercises**

**5 hours to complete**

## 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.

**5 hours to complete**

**13 videos**

**20 readings**

**4 practice exercises**

### Reviews

#### 4.8

##### TOP REVIEWS FROM MATRIX ALGEBRA FOR ENGINEERS

Very well-prepared and presented course on matrix/linear algebra operations, with emphasis on engineering considerations. Lecture notes with examples in PDF form are especially helpful.

Chasnov is outstanding! You will love the course but above all you will adore the way Chasnov marches on through the course and you are acquiring knowledge... He is a real instructor!

The professor’s dedication and explanation of the problem are great. This course is a basic course for advanced mathematics for engineers and is a good introduction to linear algebra.

Very good and straight-forward course. Very engineering-oriented (not many proofs). I had already learnt matrix algebra before so this was a good way to recall my previous knowledge.

Very informative and well organized. The faculty is very responsive when it comes to queries. This is the second course that I have taken by this faculty. Looking forward to more!

This course is not only very helpful for engineers but also helpful for under Graduate students.\n\nI like "Gram-schmidt orthogonalization process" based lecture.

I enjoyed doing all the exercises. Thank you for making the book available with the worked examples, which helped tremendously. Thank you Dr Chasnov

Yes, I spend 30 hours a week but I finished it in 2 weekends. Good course, a lot of video, going from the base to more complex subjects building up.

Very systematic course ,not a typical first course in linear algebra but brilliant overall .Extremely useful for engineers.\n\nHighly recommended!!!

It was very detailed and gave a lot of important formulas for solving problems with Matrix algebra and the instructor followed a good pace.

A wonderful course for those who want to start Matrices from scratch. The course covers all the necessary things an engineer requires.

excellent course. it helped me understand more about matrix algebra and its application. Thank you so much, Prof. Jeffrey R. Chasnov

### About The Hong Kong University of Science and Technology

## Frequently Asked Questions

When will I have access to the lectures and assignments?

Once you enroll for a Certificate, you’ll have access to all videos, quizzes, and programming assignments (if applicable). Peer review assignments can only be submitted and reviewed once your session has begun. If you choose to explore the course without purchasing, you may not be able to access certain assignments.

What will I get if I purchase the Certificate?

When you purchase a Certificate you get access to all course materials, including graded assignments. Upon completing the course, your electronic Certificate will be added to your Accomplishments page - from there, you can print your Certificate or add it to your LinkedIn profile. If you only want to read and view the course content, you can audit the course for free.

What is the refund policy?

Is financial aid available?

More questions? Visit the Learner Help Center.