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.

## About this Course

### Learner Career Outcomes

## 50%

## 33%

### What you will learn

Matrices

Systems of Linear Equations

Vector Spaces

Eigenvalues and eigenvectors

### Skills you will gain

### Learner Career Outcomes

## 50%

## 33%

### Offered by

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

HKUST - A dynamic, international research university, in relentless pursuit of excellence, leading the advance of science and technology, and educating the new generation of front-runners for Asia and the world.

## 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

### TOP REVIEWS FROM MATRIX ALGEBRA FOR ENGINEERS

Very in-depth class for matrix algebra. I am a biochemistry student and have learned this in the past but re-taking this online course again has revamped my learning for linear algebra.

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.

I have learnt the preliminary knowledge of vector spaces and eigen value problem that will help me to study my Quantum information quite well.Thank you sir for such a wonderful course.

Teacher was really friendly. Linear Algebra was a threat for me, but it is fundamental for engineering. After this course I am so much confident on linear algebra. Thank you very much.

## Frequently Asked Questions

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