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.
Matrix Algebra for Engineers
The Hong Kong University of Science and TechnologyAbout this Course
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Learner Career Outcomes
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got a tangible career benefit from this course
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Flexible deadlines
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Beginner Level
Approx. 20 hours to complete
English
Subtitles: English
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
50%
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: English
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
11 videos
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
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
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
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
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
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
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
Reviews
TOP REVIEWS FROM MATRIX ALGEBRA FOR ENGINEERS
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 PJul 18, 2020
I have learnt the preliminary knowledge of vector spaces and eigen value problem that will help me to study my Quantum information quite well.Thank you sir for such a wonderful course.
by RZOct 5, 2019
The professor’s dedication and explanation of the problem are great. This course is a basic course for advanced mathematics for engineers and is a good introduction to linear algebra.
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