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Matrix Algebra for Engineers
  • Level Foundation
  • المدة 20 ساعات hours
  • الطبع بواسطة The Hong Kong University of Science and Technology
  • Offered by

عن

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 it is recommended that students take this course after completing a university-level single variable calculus course. There are no derivatives or integrals involved, but students are expected to have a basic level of mathematical maturity. Despite this, anyone interested in learning the basics of matrix algebra is welcome to join. The course consists of 38 concise lecture videos, each followed by a few problems to solve. After each major topic, there is a short practice quiz. Solutions to the problems and practice quizzes can be found in the instructor-provided lecture notes. The course spans four weeks, and at the end of each week, there is an assessed quiz. Download the lecture notes from the link https://www.math.hkust.edu.hk/~machas/matrix-algebra-for-engineers.pdf

الوحدات

Welcome

    • 3 Readings
    • 1 Assignment
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1 Assignment

  • Diagnostic Quiz

3 Readings

  • Welcome and Course Information
  • Certificate or Audit?
  • How to Write Math in the Discussion Forums Using MathJax

Introduction to Week One

    • 1 Videos
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1 Videos

  • Week One Introduction

Matrix Definitions

    • 3 Videos
    • 8 Readings
    • 1 Assignment
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1 Assignment

  • Matrix Definitions

3 Videos

  • Definition of a Matrix | Lecture 1
  • Addition and Multiplication of Matrices | Lecture 2
  • Special Matrices | Lecture 3

8 Readings

  • Construct Some Matrices
  • Matrix Addition and Multiplication
  • AB=AC Does Not Imply B=C
  • Matrix Multiplication Does Not Commute
  • Associative Law for Matrix Multiplication
  • AB=0 When A and B Are Not zero
  • Product of Diagonal Matrices
  • Product of Triangular Matrices

Transpose and Inverses

    • 3 Videos
    • 10 Readings
    • 1 Assignment
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1 Assignment

  • Transposes and Inverses

3 Videos

  • Transpose Matrix | Lecture 4
  • Inner and Outer Products | Lecture 5
  • Inverse Matrix | Lecture 6

10 Readings

  • Transpose of a Matrix Product
  • Any Square Matrix Can Be Written as the Sum of a Symmetric and Skew-Symmetric Matrix
  • Construction of a Square Symmetric Matrix
  • Example of a Symmetric Matrix
  • Sum of the Squares of the Elements of a Matrix
  • Inverses of Two-by-Two Matrices
  • Inverse of a Matrix Product
  • Inverse of the Transpose Matrix
  • Uniqueness of the Inverse
  • Determinant as an Area

Orthogonal Matrices

    • 3 Videos
    • 6 Readings
    • 1 Assignment
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1 Assignment

  • Orthogonal Matrices

3 Videos

  • Orthogonal Matrices | Lecture 7
  • Rotation Matrices | Lecture 8
  • Permutation Matrices | Lecture 9

6 Readings

  • Product of Orthogonal Matrices
  • The Identity Matrix is Orthogonal
  • Inverse of the Rotation Matrix
  • Three-dimensional Rotation
  • Three-by-Three Permutation Matrices
  • Inverses of Three-by-Three Permutation Matrices

Quiz

    • 2 Assignment
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2 Assignment

  • Week One Assessment (audit)
  • Week One Assessment

Introduction to Week Two

    • 1 Videos
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1 Videos

  • Week Two Introduction

Gaussian Elimination

    • 3 Videos
    • 3 Readings
    • 1 Assignment
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1 Assignment

  • Gaussian Elimination

3 Videos

  • Gaussian Elimination | Lecture 10
  • Reduced Row Echelon Form | Lecture 11
  • Computing Inverses | Lecture 12

3 Readings

  • Gaussian Elimination
  • Reduced Row Echelon Form
  • Computing Inverses

LU Decomposition

    • 3 Videos
    • 3 Readings
    • 1 Assignment
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1 Assignment

  • LU Decomposition

3 Videos

  • Elementary Matrices | Lecture 13
  • LU Decomposition | Lecture 14
  • Solving (LU)x = b | Lecture 15

3 Readings

  • Elementary Matrices
  • LU Decomposition
  • Solving (LU)x = b

Quiz

    • 2 Assignment
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2 Assignment

  • Week Two Assessment (audit)
  • Week Two Assessment

Introduction to Week Three

    • 1 Videos
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1 Videos

  • Week Three Introduction

Vector Space Definitions

    • 3 Videos
    • 4 Readings
    • 1 Assignment
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1 Assignment

  • Vector Space Definitions

3 Videos

  • Vector Spaces | Lecture 16
  • Linear Independence | Lecture 17
  • Span, Basis and Dimension | Lecture 18

4 Readings

  • Zero Vector
  • Examples of Vector Spaces
  • Linear Independence
  • Orthonormal basis

Gram-Schmidt process

    • 2 Videos
    • 3 Readings
    • 1 Assignment
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1 Assignment

  • Gram-Schmidt Process

2 Videos

  • Gram-Schmidt Process | Lecture 19
  • Gram-Schmidt Process Example | Lecture 20

3 Readings

  • Gram-Schmidt Process
  • Gram-Schmidt on Three-by-One Matrices
  • Gram-Schmidt on Four-by-One Matrices

Fundamental Subspaces of a Matrix

    • 4 Videos
    • 4 Readings
    • 1 Assignment
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1 Assignment

  • Fundamental Subspaces

4 Videos

  • Null Space | Lecture 21
  • Application of the Null Space | Lecture 22
  • Column Space | Lecture 23
  • Row Space, Left Null Space and Rank | Lecture 24

4 Readings

  • Null Space
  • Underdetermined System of Linear Equations
  • Column Space
  • Fundamental Matrix Subspaces

Orthogonal Projections

    • 3 Videos
    • 3 Readings
    • 1 Assignment
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1 Assignment

  • Orthogonal Projections

3 Videos

  • Orthogonal Projections | Lecture 25
  • The Least-Squares Problem | Lecture 26
  • Solution of the Least-Squares Problem | Lecture 27

3 Readings

  • Orthogonal Projections
  • Setting Up the Least-Squares Problem
  • Line of Best Fit

Quiz

    • 2 Assignment
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2 Assignment

  • Week Three Assessment (audit)
  • Week Three Assessment

Introduction to Week Four

    • 1 Videos
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1 Videos

  • Week Four Introduction

Determinants

    • 4 Videos
    • 9 Readings
    • 1 Assignment
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1 Assignment

  • Determinants

4 Videos

  • Two-by-Two and Three-by-Three Determinants | Lecture 28
  • Laplace Expansion | Lecture 29
  • Leibniz Formula | Lecture 30
  • Properties of a Determinant | Lecture 31

9 Readings

  • Determinant of the Identity Matrix
  • Row Interchange
  • Determinant of a Matrix Product
  • Compute Determinant Using the Laplace Expansion
  • Compute Determinant Using the Leibniz Formula
  • Determinant of a Matrix With Two Equal Rows
  • Determinant is a Linear Function of Any Row
  • Determinant Can Be Computed Using Row Reduction
  • Compute Determinant Using Gaussian Elimination

The Eigenvalue Problem

    • 3 Videos
    • 4 Readings
    • 1 Assignment
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1 Assignment

  • The Eigenvalue Problem

3 Videos

  • The Eigenvalue Problem | Lecture 32
  • Finding Eigenvalues and Eigenvectors (Part A) | Lecture 33
  • Finding Eigenvalues and Eigenvectors (Part B) | Lecture 34

4 Readings

  • Characteristic Equation for a Three-by-Three Matrix
  • Eigenvalues and Eigenvectors of a Two-by-Two Matrix
  • Eigenvalues and Eigenvectors of a Three-by-Three Matrix
  • Complex Eigenvalues

Matrix Diagonalization

    • 4 Videos
    • 5 Readings
    • 1 Assignment
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1 Assignment

  • Matrix Diagonalization

4 Videos

  • Matrix Diagonalization | Lecture 35
  • Matrix Diagonalization Example | Lecture 36
  • Powers of a Matrix | Lecture 37
  • Powers of a Matrix Example | Lecture 38

5 Readings

  • Linearly Independent Eigenvectors
  • Invertibility of the Eigenvector Matrix
  • Diagonalize a Three-by-Three Matrix
  • Matrix Exponential
  • Powers of a Matrix

Quiz

    • 2 Assignment
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2 Assignment

  • Week Four Assessment (audit)
  • Week Four Assessment

Farewell

    • 1 Videos
    • 2 Readings
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1 Videos

  • Concluding Remarks

2 Readings

  • Please Rate this Course
  • Acknowledgements

Auto Summary

Matrix Algebra for Engineers is a foundational course in Maths & Statistics, designed to cover essential linear algebra concepts for engineers. Ideal for learners with a background in single-variable calculus, the course spans four weeks and includes 38 concise lecture videos, practice quizzes, and assessed weekly quizzes. Led by an expert instructor, it offers downloadable lecture notes and caters to anyone interested in matrix algebra. Available on Coursera with Starter, Professional, and Paid subscription options, this course is perfect for those seeking to strengthen their mathematical skills.

Jeffrey R. Chasnov
Instructor

Jeffrey R. Chasnov