Matrix Algebra for Engineers

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.   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.
The course contains 38 short lecture videos, with a few problems to solve after each lecture.  And after each substantial topic, there is a short practice quiz.  Solutions to the problems and practice quizzes can be found in instructor-provided lecture notes.  There are a total of four weeks in the course, and at the end of each week there is an assessed quiz.

Lecture notes can be downloaded from
http://www.math.ust.hk/~machas/matrix-algebra-for-engineers.pdf

Learner Career Outcomes

50%

started a new career after completing these courses

33%

got a tangible career benefit from this course

Shareable Certificate

Earn a Certificate upon completion

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Start instantly and learn at your own schedule.

Flexible deadlines

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Beginner Level

Approx. 20 hours to complete

English

Subtitles: French, Portuguese (Brazilian), Russian, English, Spanish

What you will learn

Matrices

Systems of Linear Equations

Vector Spaces

Eigenvalues and eigenvectors

Skills you will gain

Linear AlgebraEngineering Mathematics

Learner Career Outcomes

50%

started a new career after completing these courses

33%

got a tangible career benefit from this course

Shareable Certificate

Earn a Certificate upon completion

100% online

Start instantly and learn at your own schedule.

Flexible deadlines

Reset deadlines in accordance to your schedule.

Beginner Level

Approx. 20 hours to complete

English

Subtitles: French, Portuguese (Brazilian), Russian, English, Spanish

Instructor

Instructor rating

4.82/5 (486 Ratings)

Jeffrey R. Chasnov
Top Instructor

Professor

Department of Mathematics

94,012 Learners

4 Courses

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

Content Rating97%(6,762 ratings)

Week

Week 1

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 (Total 84 min), 25 readings, 5 quizzes

11 videos

Promotional Video4m

Introduction1m

Definition of a Matrix | Lecture 17m

Addition and Multiplication of Matrices | Lecture 210m

Special Matrices | Lecture 39m

Transpose Matrix | Lecture 49m

Inner and Outer Products | Lecture 59m

Inverse Matrix | Lecture 612m

Orthogonal Matrices | Lecture 74m

Rotation Matrices | Lecture 88m

Permutation Matrices | Lecture 96m

25 readings

Welcome and Course Information1m

How to Write Math in the Discussions Using MathJax1m

Construct Some Matrices5m

Matrix Addition and Multiplication5m

AB=AC Does Not Imply B=C5m

Matrix Multiplication Does Not Commute5m

Associative Law for Matrix Multiplication10m

AB=0 When A and B Are Not zero10m

Product of Diagonal Matrices5m

Product of Triangular Matrices10m

Transpose of a Matrix Product10m

Any Square Matrix Can Be Written as the Sum of a Symmetric and Skew-Symmetric Matrix5m

Construction of a Square Symmetric Matrix5m

Example of a Symmetric Matrix10m

Sum of the Squares of the Elements of a Matrix10m

Inverses of Two-by-Two Matrices5m

Inverse of a Matrix Product10m

Inverse of the Transpose Matrix10m

Uniqueness of the Inverse10m

Product of Orthogonal Matrices5m

The Identity Matrix is Orthogonal5m

Inverse of the Rotation Matrix5m

Three-dimensional Rotation10m

Three-by-Three Permutation Matrices10m

Inverses of Three-by-Three Permutation Matrices10m

5 practice exercises

Diagnostic Quiz5m

Matrix Definitions10m

Transposes and Inverses10m

Orthogonal Matrices10m

Week One Assessment30m

Week

Week 2

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 (Total 71 min), 6 readings, 3 quizzes

7 videos

Introduction1m

Gaussian Elimination | Lecture 1014m

Reduced Row Echelon Form | Lecture 118m

Computing Inverses | Lecture 1213m

Elementary Matrices | Lecture 1311m

LU Decomposition | Lecture 1410m

Solving (LU)x = b | Lecture 1511m

6 readings

Gaussian Elimination15m

Reduced Row Echelon Form15m

Computing Inverses15m

Elementary Matrices5m

LU Decomposition15m

Solving (LU)x = b10m

3 practice exercises

Gaussian Elimination20m

LU Decomposition15m

Week Two Assessment30m

Week

Week 3

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 (Total 140 min), 14 readings, 5 quizzes

13 videos

Introduction1m

Vector Spaces | Lecture 167m

Linear Independence | Lecture 179m

Span, Basis and Dimension | Lecture 1810m

Gram-Schmidt Process | Lecture 1913m

Gram-Schmidt Process Example | Lecture 209m

Null Space | Lecture 2112m

Application of the Null Space | Lecture 2214m

Column Space | Lecture 239m

Row Space, Left Null Space and Rank | Lecture 2414m

Orthogonal Projections | Lecture 2511m

The Least-Squares Problem | Lecture 2610m

Solution of the Least-Squares Problem | Lecture 2715m

14 readings

Zero Vector5m

Examples of Vector Spaces5m

Linear Independence5m

Orthonormal basis5m

Gram-Schmidt Process5m

Gram-Schmidt on Three-by-One Matrices5m

Gram-Schmidt on Four-by-One Matrices10m

Null Space10m

Underdetermined System of Linear Equations10m

Column Space5m

Fundamental Matrix Subspaces10m

Orthogonal Projections5m

Setting Up the Least-Squares Problem5m

Line of Best Fit5m

5 practice exercises

Vector Space Definitions15m

Gram-Schmidt Process15m

Fundamental Subspaces15m

Orthogonal Projections15m

Week Three Assessment30m

Week

Week 4

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 (Total 120 min), 20 readings, 4 quizzes

13 videos

Introduction1m

Two-by-Two and Three-by-Three Determinants | Lecture 288m

Laplace Expansion | Lecture 2913m

Leibniz Formula | Lecture 3011m

Properties of a Determinant | Lecture 3115m

The Eigenvalue Problem | Lecture 3212m

Finding Eigenvalues and Eigenvectors (1) | Lecture 3310m

Finding Eigenvalues and Eigenvectors (2) | Lecture 347m

Matrix Diagonalization | Lecture 359m

Matrix Diagonalization Example | Lecture 3615m

Powers of a Matrix | Lecture 375m

Powers of a Matrix Example | Lecture 386m

Concluding Remarks3m

20 readings

Determinant of the Identity Matrix5m

Row Interchange5m

Determinant of a Matrix Product10m

Compute Determinant Using the Laplace Expansion5m

Compute Determinant Using the Leibniz Formula5m

Determinant of a Matrix With Two Equal Rows5m

Determinant is a Linear Function of Any Row5m

Determinant Can Be Computed Using Row Reduction5m

Compute Determinant Using Gaussian Elimination5m

Characteristic Equation for a Three-by-Three Matrix10m

Eigenvalues and Eigenvectors of a Two-by-Two Matrix5m

Eigenvalues and Eigenvectors of a Three-by-Three Matrix10m

Complex Eigenvalues5m

Linearly Independent Eigenvectors5m

Invertibility of the Eigenvector Matrix5m

Diagonalize a Three-by-Three Matrix10m

Matrix Exponential5m

Powers of a Matrix10m

Please Rate this Course1m

Acknowledgments

4 practice exercises

Determinants15m

The Eigenvalue Problem15m

Matrix Diagonalization15m

Week Four Assessment30m

Frequently Asked Questions

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Will I earn university credit for completing the Course?
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Matrix Algebra for Engineers