About this Course
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Beginner Level

Approx. 13 hours to complete

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

English

Subtitles: English

What you will learn

  • Check

    Matrices

  • Check

    Systems of Linear Equations

  • Check

    Vector Spaces

  • Check

    Eigenvalues and eigenvectors

Skills you will gain

Eigenvalues And EigenvectorsGaussian EliminationEngineering MathematicsMatricesLinear Algebra

100% online

Start instantly and learn at your own schedule.

Flexible deadlines

Reset deadlines in accordance to your schedule.

Beginner Level

Approx. 13 hours to complete

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

English

Subtitles: English

Syllabus - What you will learn from this course

Week
1
7 hours to complete

MATRICES

11 videos (Total 84 min), 25 readings, 5 quizzes
11 videos
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
25 readings
Welcome and Course Information5m
Get to Know Your Classmates10m
Practice: Construct Some Matrices10m
Practice: Matrix Addition and Multiplication1m
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
5 practice exercises
Diagnostic Quiz10m
Matrix Definitions15m
Transposes and Inverses15m
Orthogonal Matrices15m
Week One50m
Week
2
4 hours to complete

SYSTEMS OF LINEAR EQUATIONS

7 videos (Total 71 min), 6 readings, 3 quizzes
7 videos
Gaussian Elimination14m
Reduced Row Echelon Form8m
Computing Inverses13m
Elementary Matrices11m
LU Decomposition10m
Solving (LU)x = b11m
6 readings
Practice: Gaussian Elimination10m
Practice: Reduced Row Echelon Form10m
Practice: Computing Inverses10m
Practice: Elementary Matrices10m
Practice: LU Decomposition10m
Practice: Solving (LU)x = b10m
3 practice exercises
Gaussian Elimination25m
LU Decomposition30m
Week Two30m
Week
3
7 hours to complete

VECTOR SPACES

13 videos (Total 140 min), 14 readings, 5 quizzes
13 videos
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
14 readings
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
5 practice exercises
Vector Space Definitions15m
Gram-Schmidt Process30m
Fundamental Subspaces30m
Orthogonal Projections30m
Week Three50m
Week
4
7 hours to complete

EIGENVALUES AND EIGENVECTORS

13 videos (Total 120 min), 20 readings, 4 quizzes
13 videos
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
20 readings
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
Acknowledgments1m
4 practice exercises
Determinants15m
The Eigenvalue Problem20m
Matrix Diagonalization30m
Week Four50m
4.8
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Top reviews from Matrix Algebra for Engineers

By JMar 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 RHNov 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.

Instructor

Avatar

Jeffrey R. Chasnov

Professor
Department of Mathematics

About 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....

Frequently Asked Questions

  • 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.

  • 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.

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