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.
Offered By
Matrix Algebra for Engineers
The Hong Kong University of Science and TechnologyAbout this Course
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Beginner Level
Approx. 20 hours to complete
English
Subtitles: Arabic, French, Portuguese (European), Italian, Vietnamese, German, Russian, English, Spanish
What you will learn
Matrices
Systems of Linear Equations
Vector Spaces
Eigenvalues and eigenvectors
Skills you will gain
- Linear Algebra
- Engineering Mathematics
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.
Beginner Level
Approx. 20 hours to complete
English
Subtitles: Arabic, French, Portuguese (European), Italian, Vietnamese, German, Russian, English, Spanish
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
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
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
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
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
Reviews
TOP REVIEWS FROM MATRIX ALGEBRA FOR ENGINEERS
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 RHNov 6, 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.
by DLApr 30, 2020
Very in-depth class for matrix algebra. I am a biochemistry student and have learned this in the past but re-taking this online course again has revamped my learning for linear algebra.
by AINov 8, 2020
Teacher was really friendly. Linear Algebra was a threat for me, but it is fundamental for engineering. After this course I am so much confident on linear algebra. Thank you very much.
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