Offered By

The Hong Kong University of Science and Technology

About this Course

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This course is all about matrices, and concisely covers the linear algebra that an engineer should know. We define matrices and how to add and multiply them, and introduce some special types of matrices. We describe the Gaussian elimination algorithm used to solve systems of linear equations and the corresponding LU decomposition of a matrix. We explain the concept of vector spaces and define the main vocabulary of linear algebra. We develop the theory of determinants and use it to solve the eigenvalue problem.
After each video, there are problems to solve and I have tried to choose problems that exemplify the main idea of the lecture. I try to give enough problems for students to solidify their understanding of the material, but not so many that students feel overwhelmed and drop out. I do encourage students to attempt the given problems, but if they get stuck, full solutions can be found in the lecture notes for the course.
The mathematics in this matrix algebra course is presented at the level of an advanced high school student, but typically students would take this course after completing a university-level single variable calculus course. There are no derivatives or integrals in this course, but student's are expected to have a certain level of mathematical maturity. Nevertheless, anyone who wants to learn the basics of matrix algebra is welcome to join.
Lecture notes may be downloaded at
https://bookboon.com/en/matrix-algebra-for-engineers-ebook
or
http://www.math.ust.hk/~machas/matrix-algebra-for-engineers.pdf
Watch the course overview video at
https://youtu.be/IZcyZHomFQc

Start instantly and learn at your own schedule.

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Suggested: 4 weeks of study, 3-4 hours/week...

Subtitles: English

Start instantly and learn at your own schedule.

Reset deadlines in accordance to your schedule.

Suggested: 4 weeks of study, 3-4 hours/week...

Subtitles: English

Week

1In this week's lectures, we learn about matrices. Matrices are rectangular arrays of numbers or other mathematical objects and are fundamental to engineering mathematics. We will 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. ...

11 videos (Total 84 min), 25 readings, 5 quizzes

Introduction1m

Definition of a Matrix7m

Addition and Multiplication of Matrices10m

Special Matrices9m

Transpose Matrix9m

Inner and Outer Products9m

Inverse Matrix12m

Orthogonal Matrices4m

Rotation Matrices8m

Permutation Matrices6m

Welcome and Course Information5m

Get to Know Your Classmates10m

Practice: Construct Some Matrices10m

Practice: Matrix Addition and Multiplication10m

Practice: AB=AC Does Not Imply B=C10m

Practice: Matrix Multiplication Does Not Commute10m

Practice: Associative Law for Matrix Multiplication10m

Practice: AB=0 When A and B Are Not zero10m

Practice: Product of Diagonal Matrices10m

Practice: Product of Triangular Matrices10m

Practice: Transpose of a Matrix Product10m

Practice: Any Square Matrix Can Be Written as the Sum of a Symmetric and Skew-Symmetric Matrix10m

Practice: Construction of a Square Symmetric Matrix10m

Practice: Example of a Symmetric Matrix10m

Practice: Sum of the Squares of the Elements of a Matrix10m

Practice: Inverses of Two-by-Two Matrices10m

Practice: Inverse of a Matrix Product10m

Practice: Inverse of the Transpose Matrix10m

Practice: Uniqueness of the Inverse10m

Practice: Product of Orthogonal Matrices10m

Practice: The Identity Matrix is Orthogonal10m

Practice: Inverse of the Rotation Matrix10m

Practice: Three-dimensional Rotation10m

Practice: Three-by-Three Permutation Matrices10m

Practice: Inverses of Three-by-Three Permutation Matrices10m

Diagnostic Quiz10m

Matrix Definitions10m

Transposes and Inverses10m

Orthogonal Matrices10m

Week One30m

Week

2In this week's lectures, we learn about solving a system of linear equations. A system of linear equations can be written in matrix form, and we can solve using Gaussian elimination. We will learn how to bring a matrix to reduced row echelon form, and how this can be used to compute a matrix inverse. We will also learn how to find the LU decomposition of a matrix, and how to use this decomposition to efficiently solve a system of linear equations....

7 videos (Total 71 min), 6 readings, 3 quizzes

Gaussian Elimination14m

Reduced Row Echelon Form8m

Computing Inverses13m

Elementary Matrices11m

LU Decomposition10m

Solving (LU)x = b11m

Practice: Gaussian Elimination10m

Practice: Reduced Row Echelon Form10m

Practice: Computing Inverses10m

Practice: Elementary Matrices10m

Practice: LU Decomposition10m

Practice: Solving (LU)x = b10m

Gaussian Elimination10m

LU Decomposition10m

Week Two30m

Week

3In this week's lectures, we learn about 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 will learn some of the vocabulary and phrases of linear algebra, such as linear independence, span, basis and dimension. We will 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....

13 videos (Total 140 min), 14 readings, 5 quizzes

Vector Spaces7m

Linear Independence9m

Span, Basis and Dimension10m

Gram-Schmidt Process13m

Gram-Schmidt Process Example9m

Null Space12m

Application of the Null Space14m

Column Space9m

Row Space, Left Null Space and Rank14m

Orthogonal Projections11m

The Least-Squares Problem10m

Solution of the Least-Squares Problem15m

Practice: Zero Vector10m

Practice: Examples of Vector Spaces10m

Practice: Linear Independence10m

Practice: Orthonormal basis10m

Practice: Gram-Schmidt Process10m

Practice: Gram-Schmidt on Three-by-One Matrices10m

Practice: Gram-Schmidt on Four-by-One Matrices10m

Practice: Null Space10m

Practice: Underdetermined System of Linear Equations10m

Practice: Column Space10m

Practice: Fundamental Matrix Subspaces10m

Practice: Orthogonal Projections10m

Practice: Setting Up the Least-Squares Problem10m

Practice: Line of Best Fit10m

Vector Space Definitions10m

Gram-Schmidt Process10m

Fundamental Subspaces10m

Orthogonal Projections10m

Week Three30m

Week

4In this week's lectures, we will learn about determinants and the eigenvalue problem. We will learn how to compute determinants using a Laplace expansion, the Leibniz formula, or by row or column elimination. We will formulate the eigenvalue problem and learn how to find the eigenvalues and eigenvectors of a matrix. We will 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. ...

13 videos (Total 120 min), 20 readings, 4 quizzes

Two-by-Two and Three-by-Three Determinants8m

Laplace Expansion13m

Leibniz Formula11m

Properties of a Determinant15m

The Eigenvalue Problem12m

Finding Eigenvalues and Eigenvectors (1)10m

Finding Eigenvalues and Eigenvectors (2)7m

Matrix Diagonalization9m

Matrix Diagonalization Example15m

Powers of a Matrix5m

Powers of a Matrix Example6m

Concluding Remarks3m

Practice: Determinant of the Identity Matrix10m

Practice: Row Interchange10m

Practice: Determinant of a Matrix Product10m

Practice: Compute Determinant Using the Laplace Expansion10m

Practice: Compute Determinant Using the Leibniz Formula10m

Practice: Determinant of a Matrix With Two Equal Rows10m

Practice: Determinant is a Linear Function of Any Row10m

Practice: Determinant Can Be Computed Using Row Reduction10m

Practice: Compute Determinant Using Gaussian Elimination10m

Practice: Characteristic Equation for a Three-by-Three Matrix10m

Practice: Eigenvalues and Eigenvectors of a Two-by-Two Matrix10m

Practice: Eigenvalues and Eigenvectors of a Three-by-Three Matrix10m

Practice: Complex Eigenvalues10m

Practice: Linearly Independent Eigenvectors10m

Practice: Invertibility of the Eigenvector Matrix10m

Practice: Diagonalize a Three-by-Three Matrix10m

Practice: Matrix Exponential10m

Practice: Powers of a Matrix10m

Please Rate this Course10m

Acknowledgements1m

Determinants10m

The Eigenvalue Problem10m

Matrix Diagonalization10m

Week Four30m

4.8

40 Reviewsstarted a new career after completing these courses

got a tangible career benefit from this course

By J•Mar 12th 2019

Es muy bueno el curso de verdad que lo recomiendo mucho para todos aquellos estudiantes que cursan Álgebra Lineal ya que tiene todas las herramientas necesarias para aprender esa materia

By RH•Nov 7th 2018

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.

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....

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