This course is part of the Mathematics for Engineers Specialization

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3,926 ratings

Jeffrey R. Chasnov

Top Instructor

76,940 already enrolled

Offered By

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 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

And watch the promotional video from the link
https://youtu.be/IZcyZHomFQc

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Coursera Labs

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Course 1 of 5 in the

Mathematics for Engineers Specialization

Beginner Level

Approx. 19 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

Start instantly and learn at your own schedule.

Coursera Labs

Includes hands on learning projects.

Learn more about Coursera Labs

Course 1 of 5 in the

Mathematics for Engineers Specialization

Beginner Level

Approx. 19 hours to complete

English

Could your company benefit from training employees on in-demand skills?

Try Coursera for Business

Instructor

Instructor rating

4.85/5 (1,249 Ratings)

Jeffrey R. Chasnov
Top Instructor

Professor

Department of Mathematics

171,854 Learners

16 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%(13,025 ratings)

Week1

Week 1

6 hours to complete

MATRICES

6 hours to complete

10 videos (Total 79 min), 27 readings, 6 quizzes

10 videos

27 readings

Welcome and Course Information1mCertificate or Audit?1mHow to Write Math in the Discussion Forums Using MathJax1mConstruct Some Matrices5mMatrix Addition and Multiplication5mAB=AC Does Not Imply B=C5mMatrix Multiplication Does Not Commute5mAssociative Law for Matrix Multiplication10mAB=0 When A and B Are Not zero10mProduct of Diagonal Matrices5mProduct of Triangular Matrices10mTranspose of a Matrix Product10mAny Square Matrix Can Be Written as the Sum of a Symmetric and Skew-Symmetric Matrix5mConstruction of a Square Symmetric Matrix5mExample of a Symmetric Matrix10mSum of the Squares of the Elements of a Matrix10mInverses of Two-by-Two Matrices5mInverse of a Matrix Product10mInverse of the Transpose Matrix10mUniqueness of the Inverse10mDeterminant as an Area10mProduct of Orthogonal Matrices5mThe Identity Matrix is Orthogonal5mInverse of the Rotation Matrix5mThree-dimensional Rotation10mThree-by-Three Permutation Matrices10mInverses of Three-by-Three Permutation Matrices10m

6 practice exercises

Diagnostic Quiz5mMatrix Definitions10mTransposes and Inverses10mOrthogonal Matrices10mWeek One Assessment (audit)Week One Assessment30m

Week2

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

6 readings

Gaussian Elimination15mReduced Row Echelon Form15mComputing Inverses15mElementary Matrices5mLU Decomposition15mSolving (LU)x = b10m

4 practice exercises

Gaussian Elimination20mLU Decomposition15mWeek Two Assessment (audit)Week Two Assessment30m

Week3

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

14 readings

Zero Vector5mExamples of Vector Spaces5mLinear Independence5mOrthonormal basis5mGram-Schmidt Process5mGram-Schmidt on Three-by-One Matrices5mGram-Schmidt on Four-by-One Matrices10mNull Space10mUnderdetermined System of Linear Equations10mColumn Space5mFundamental Matrix Subspaces10mOrthogonal Projections5mSetting Up the Least-Squares Problem5mLine of Best Fit5m

6 practice exercises

Vector Space Definitions15mGram-Schmidt Process15mFundamental Subspaces15mOrthogonal Projections15mWeek Three Assessment (audit)Week Three Assessment30m

Week4

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, and by row or column elimination. We also learn how to diagonalize a matrix using its eigenvalues and eigenvectors, and how this can be used to easily calculate a matrix raised to a power.

5 hours to complete

13 videos (Total 119 min), 20 readings, 5 quizzes

13 videos

Week Four Introduction51sTwo-by-Two and Three-by-Three Determinants | Lecture 288mLaplace Expansion | Lecture 2913mLeibniz Formula | Lecture 3011mProperties of a Determinant | Lecture 3115mThe Eigenvalue Problem | Lecture 3212mFinding Eigenvalues and Eigenvectors (Part A) | Lecture 3310mFinding Eigenvalues and Eigenvectors (Part B) | Lecture 347mMatrix Diagonalization | Lecture 359mMatrix Diagonalization Example | Lecture 3615mPowers of a Matrix | Lecture 375mPowers of a Matrix Example | Lecture 386mConcluding Remarks1m

20 readings

Determinant of the Identity Matrix5mRow Interchange5mDeterminant of a Matrix Product10mCompute Determinant Using the Laplace Expansion5mCompute Determinant Using the Leibniz Formula5mDeterminant of a Matrix With Two Equal Rows5mDeterminant is a Linear Function of Any Row5mDeterminant Can Be Computed Using Row Reduction5mCompute Determinant Using Gaussian Elimination5mCharacteristic Equation for a Three-by-Three Matrix10mEigenvalues and Eigenvectors of a Two-by-Two Matrix5mEigenvalues and Eigenvectors of a Three-by-Three Matrix10mComplex Eigenvalues5mLinearly Independent Eigenvectors5mInvertibility of the Eigenvector Matrix5mDiagonalize a Three-by-Three Matrix10mMatrix Exponential5mPowers of a Matrix10mPlease Rate this Course1mAcknowledgements

5 practice exercises

Determinants15mThe Eigenvalue Problem15mMatrix Diagonalization15mWeek Four Assessment (audit)Week Four Assessment30m

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TOP REVIEWS FROM MATRIX ALGEBRA FOR ENGINEERS

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 MRJun 13, 2020

All the concepts and techniques are clearly explained. There are very good exercises for each lesson. very good course. Thanks to Professor Jeff Chasnov and Coursera people.

by JRAug 4, 2021

This is a carefully sequenced, content-rich introduction to Matrices; beware skimming over details: eg. the use of matrix formalism to solve the least squares problem is little short of magic.

by OTJan 4, 2020

Very good and straight-forward course. Very engineering-oriented (not many proofs). I had already learnt matrix algebra before so this was a good way to recall my previous knowledge.

View all reviews

About the Mathematics for Engineers Specialization

This specialization was developed for engineering students to self-study engineering mathematics. We expect students to already be familiar with single variable calculus and computer programming. Through this specialization, students will learn matrix algebra, differential equations, vector calculus, numerical methods, and MATLAB programming. This will provide them with the tools to effectively apply mathematics to engineering problems and be well-equipped to pursue a degree in engineering. To get a better understanding of what this specialization has to offer, be sure to watch the Promotional Video!

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.
Is financial aid available?
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

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