This course is part of the Mathematics for Engineers Specialization

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Jeffrey R. Chasnov

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Mathematics for Engineers SpecializationThe 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.

Download the lecture notes:
http://www.math.ust.hk/~machas/matrix-algebra-for-engineers.pdf

Watch the promotional video: 
https://youtu.be/IZcyZHomFQc

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Course 1 of 5 in the

Mathematics for Engineers Specialization

Beginner Level

Approx. 20 hours to complete

English

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What you will learn

Matrices
Systems of Linear Equations
Vector Spaces
Eigenvalues and eigenvectors

Flexible deadlines

Reset deadlines in accordance to your schedule.

Shareable Certificate

Earn a Certificate upon completion

100% online

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Course 1 of 5 in the

Mathematics for Engineers Specialization

Beginner Level

Approx. 20 hours to complete

English

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Instructor

Instructor rating

4.85/5 (1,233 Ratings)

Jeffrey R. Chasnov
Top Instructor

Professor

Department of Mathematics

167,521 Learners

6 Courses

Offered by

The Hong Kong University of Science and Technology

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Syllabus - What you will learn from this course

Content Rating97%(12,902 ratings)

Week

Week 1

6 hours to complete

MATRICES

6 hours to complete

11 videos (Total 84 min), 27 readings, 6 quizzes

11 videos

Promotional Video4m

Week One Introduction59s

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

27 readings

Welcome and Course Information1m

Certificate or Audit?1m

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

Determinant as an Area10m

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

6 practice exercises

Diagnostic Quiz5m

Matrix Definitions10m

Transposes and Inverses10m

Orthogonal Matrices10m

Week One Assessment (audit)

Week One Assessment30m

Week

Week 2

4 hours to complete

SYSTEMS OF LINEAR EQUATIONS

4 hours to complete

7 videos (Total 70 min), 6 readings, 4 quizzes

7 videos

Week Two Introduction48s

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

4 practice exercises

Gaussian Elimination20m

LU Decomposition15m

Week Two Assessment (audit)

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, 6 quizzes

13 videos

Week Three Introduction54s

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

6 practice exercises

Vector Space Definitions15m

Gram-Schmidt Process15m

Fundamental Subspaces15m

Orthogonal Projections15m

Week Three Assessment (audit)

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 119 min), 20 readings, 5 quizzes

13 videos

Week Four Introduction51s

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 (Part A) | Lecture 3310m

Finding Eigenvalues and Eigenvectors (Part B) | 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 Remarks1m

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

Acknowledgements

5 practice exercises

Determinants15m

The Eigenvalue Problem15m

Matrix Diagonalization15m

Week Four Assessment (audit)

Week Four Assessment30m

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TOP REVIEWS FROM MATRIX ALGEBRA FOR ENGINEERS

by JPJan 12, 2021

It teaches quite a lot about the fundamentals of linear algebra. I do wish that there were more examples but maybe it also depends on the learner if they want to learn more problems.

by MSJun 8, 2020

An excellent course to strengthen the concepts! The course covers most of the important topics in matrix algebra and the videos help in understanding the concepts in an easier way!

by UBJun 7, 2020

Very good course its really useful and I learn so much through this course , thanks for all who is help us to learn more and more . The videos made me understand all the concepts.

by SAApr 5, 2019

Very informative and well organized. The faculty is very responsive when it comes to queries. This is the second course that I have taken by this faculty. Looking forward to more!

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About the Mathematics for Engineers Specialization

Frequently Asked Questions

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Access to lectures and assignments depends on your type of enrollment. If you take a course in audit mode, you will be able to see most course materials for free. To access graded assignments and to earn a Certificate, you will need to purchase the Certificate experience, during or after your audit. If you don't see the audit option:
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The course may offer 'Full Course, No Certificate' instead. This option lets you see all course materials, submit required assessments, and get a final grade. This also means that you will not be able to purchase a Certificate experience.
What will I get if I subscribe to this Specialization?
When you enroll in the course, you get access to all of the courses in the Specialization, and you earn a certificate when you complete the work. 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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Yes. In select learning programs, you can apply for financial aid or a scholarship if you can’t afford the enrollment fee. If fin aid or scholarship is available for your learning program selection, you’ll find a link to apply on the description page.

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Matrix Algebra for Engineers

About this Course

What you will learn

Instructor

Jeffrey R. Chasnov
Top Instructor

Offered by

The Hong Kong University of Science and Technology

Syllabus - What you will learn from this course

MATRICES

SYSTEMS OF LINEAR EQUATIONS

VECTOR SPACES

EIGENVALUES AND EIGENVECTORS

Reviews

TOP REVIEWS FROM MATRIX ALGEBRA FOR ENGINEERS

About the Mathematics for Engineers Specialization

Frequently Asked Questions

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Matrix Algebra for Engineers

About this Course

What you will learn

Instructor

Jeffrey R. ChasnovTop Instructor

Offered by

The Hong Kong University of Science and Technology

Syllabus - What you will learn from this course

MATRICES

SYSTEMS OF LINEAR EQUATIONS

VECTOR SPACES

EIGENVALUES AND EIGENVECTORS

Reviews

TOP REVIEWS FROM MATRIX ALGEBRA FOR ENGINEERS

About the Mathematics for Engineers Specialization

Frequently Asked Questions

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Start or advance your career

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Jeffrey R. Chasnov
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