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#### 100% online

Start instantly and learn at your own schedule.

#### Approx. 12 hours to complete

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

#### English

Subtitles: English

#### 100% online

Start instantly and learn at your own schedule.

#### Approx. 12 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

In 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
11 videos
Introduction1m
Definition of a Matrix7m
Special Matrices9m
Transpose Matrix9m
Inner and Outer Products9m
Inverse Matrix12m
Orthogonal Matrices4m
Rotation Matrices8m
Permutation Matrices6m
Welcome and Course Information5m
Practice: Construct Some Matrices10m
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 Definitions10m
Transposes and Inverses10m
Orthogonal Matrices10m
Week One30m
Week
2
3 hours to complete

## SYSTEMS OF LINEAR EQUATIONS

In 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
7 videos
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
3 practice exercises
Gaussian Elimination10m
LU Decomposition10m
Week Two30m
Week
3
6 hours to complete

## VECTOR SPACES

In 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
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
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 Definitions10m
Gram-Schmidt Process10m
Fundamental Subspaces10m
Orthogonal Projections10m
Week Three30m
Week
4
6 hours to complete

## EIGENVALUES AND EIGENVECTORS

In 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
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
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
Acknowledgements1m
4 practice exercises
Determinants10m
The Eigenvalue Problem10m
Matrix Diagonalization10m
Week Four30m
4.8
39 Reviews

## 50%

started a new career after completing these courses

## 50%

got a tangible career benefit from this course

### Top Reviews

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

### 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....