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.
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Matrix Algebra for Engineers
Гонконгский университет науки и технологий
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Начальный уровень
Прибл. 20 часа на выполнение
Английский
Субтитры: Английский
Чему вы научитесь
Matrices
Systems of Linear Equations
Vector Spaces
Eigenvalues and eigenvectors
Приобретаемые навыки
Linear AlgebraEngineering Mathematics
Карьерные результаты учащихся
50%
начал новую карьеру, пройдя эти курсы
50%
получил значимые преимущества в карьере благодаря этому курсу
Сертификат, ссылками на который можно делиться с другими людьми
Получите сертификат по завершении
100% онлайн
Начните сейчас и учитесь по собственному графику.
Гибкие сроки
Назначьте сроки сдачи в соответствии со своим графиком.
Начальный уровень
Прибл. 20 часа на выполнение
Английский
Субтитры: Английский
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Гонконгский университет науки и технологий
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.
Программа курса: что вы изучите
5 ч. на завершение
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 ч. на завершение
11 видео ((всего 84 мин.)), 25 материалов для самостоятельного изучения, 5 тестов
11 видео
Introduction1мин
Definition of a Matrix | Lecture 17мин
Addition and Multiplication of Matrices | Lecture 210мин
Special Matrices | Lecture 39мин
Transpose Matrix | Lecture 49мин
Inner and Outer Products | Lecture 59мин
Inverse Matrix | Lecture 612мин
Orthogonal Matrices | Lecture 74мин
Rotation Matrices | Lecture 88мин
Permutation Matrices | Lecture 96мин
25 материала для самостоятельного изучения
Welcome and Course Information1мин
How to Write Math in the Discussions Using MathJax1мин
Construct Some Matrices5мин
Matrix Addition and Multiplication5мин
AB=AC Does Not Imply B=C5мин
Matrix Multiplication Does Not Commute5мин
Associative Law for Matrix Multiplication10мин
AB=0 When A and B Are Not zero10мин
Product of Diagonal Matrices5мин
Product of Triangular Matrices10мин
Transpose of a Matrix Product10мин
Any Square Matrix Can Be Written as the Sum of a Symmetric and Skew-Symmetric Matrix5мин
Construction of a Square Symmetric Matrix5мин
Example of a Symmetric Matrix10мин
Sum of the Squares of the Elements of a Matrix10мин
Inverses of Two-by-Two Matrices5мин
Inverse of a Matrix Product10мин
Inverse of the Transpose Matrix10мин
Uniqueness of the Inverse10мин
Product of Orthogonal Matrices5мин
The Identity Matrix is Orthogonal5мин
Inverse of the Rotation Matrix5мин
Three-dimensional Rotation10мин
Three-by-Three Permutation Matrices10мин
Inverses of Three-by-Three Permutation Matrices10мин
5 практического упражнения
Diagnostic Quiz5мин
Matrix Definitions10мин
Transposes and Inverses10мин
Orthogonal Matrices10мин
Week One Assessment30мин
4 ч. на завершение
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 ч. на завершение
7 видео ((всего 71 мин.)), 6 материалов для самостоятельного изучения, 3 тестов
7 видео
Introduction1мин
Gaussian Elimination | Lecture 1014мин
Reduced Row Echelon Form | Lecture 118мин
Computing Inverses | Lecture 1213мин
Elementary Matrices | Lecture 1311мин
LU Decomposition | Lecture 1410мин
Solving (LU)x = b | Lecture 1511мин
6 материала для самостоятельного изучения
Gaussian Elimination15мин
Reduced Row Echelon Form15мин
Computing Inverses15мин
Elementary Matrices5мин
LU Decomposition15мин
Solving (LU)x = b10мин
3 практического упражнения
Gaussian Elimination20мин
LU Decomposition15мин
Week Two Assessment30мин
5 ч. на завершение
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 ч. на завершение
13 видео ((всего 140 мин.)), 14 материалов для самостоятельного изучения, 5 тестов
13 видео
Introduction1мин
Vector Spaces | Lecture 167мин
Linear Independence | Lecture 179мин
Span, Basis and Dimension | Lecture 1810мин
Gram-Schmidt Process | Lecture 1913мин
Gram-Schmidt Process Example | Lecture 209мин
Null Space | Lecture 2112мин
Application of the Null Space | Lecture 2214мин
Column Space | Lecture 239мин
Row Space, Left Null Space and Rank | Lecture 2414мин
Orthogonal Projections | Lecture 2511мин
The Least-Squares Problem | Lecture 2610мин
Solution of the Least-Squares Problem | Lecture 2715мин
14 материала для самостоятельного изучения
Zero Vector5мин
Examples of Vector Spaces5мин
Linear Independence5мин
Orthonormal basis5мин
Gram-Schmidt Process5мин
Gram-Schmidt on Three-by-One Matrices5мин
Gram-Schmidt on Four-by-One Matrices10мин
Null Space10мин
Underdetermined System of Linear Equations10мин
Column Space5мин
Fundamental Matrix Subspaces10мин
Orthogonal Projections5мин
Setting Up the Least-Squares Problem5мин
Line of Best Fit5мин
5 практического упражнения
Vector Space Definitions15мин
Gram-Schmidt Process15мин
Fundamental Subspaces15мин
Orthogonal Projections15мин
Week Three Assessment30мин
5 ч. на завершение
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 ч. на завершение
13 видео ((всего 120 мин.)), 20 материалов для самостоятельного изучения, 4 тестов
13 видео
Introduction1мин
Two-by-Two and Three-by-Three Determinants | Lecture 288мин
Laplace Expansion | Lecture 2913мин
Leibniz Formula | Lecture 3011мин
Properties of a Determinant | Lecture 3115мин
The Eigenvalue Problem | Lecture 3212мин
Finding Eigenvalues and Eigenvectors (1) | Lecture 3310мин
Finding Eigenvalues and Eigenvectors (2) | Lecture 347мин
Matrix Diagonalization | Lecture 359мин
Matrix Diagonalization Example | Lecture 3615мин
Powers of a Matrix | Lecture 375мин
Powers of a Matrix Example | Lecture 386мин
Concluding Remarks3мин
20 материала для самостоятельного изучения
Determinant of the Identity Matrix5мин
Row Interchange5мин
Determinant of a Matrix Product10мин
Compute Determinant Using the Laplace Expansion5мин
Compute Determinant Using the Leibniz Formula5мин
Determinant of a Matrix With Two Equal Rows5мин
Determinant is a Linear Function of Any Row5мин
Determinant Can Be Computed Using Row Reduction5мин
Compute Determinant Using Gaussian Elimination5мин
Characteristic Equation for a Three-by-Three Matrix10мин
Eigenvalues and Eigenvectors of a Two-by-Two Matrix5мин
Eigenvalues and Eigenvectors of a Three-by-Three Matrix10мин
Complex Eigenvalues5мин
Linearly Independent Eigenvectors5мин
Invertibility of the Eigenvector Matrix5мин
Diagonalize a Three-by-Three Matrix10мин
Matrix Exponential5мин
Powers of a Matrix10мин
Please Rate this Course1мин
Acknowledgments
4 практического упражнения
Determinants15мин
The Eigenvalue Problem15мин
Matrix Diagonalization15мин
Week Four Assessment30мин
Рецензии
Лучшие отзывы о курсе MATRIX ALGEBRA FOR ENGINEERS
от партнера 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.
от партнера CGMar 2, 2019
Chasnov is outstanding! You will love the course but above all you will adore the way Chasnov marches on through the course and you are acquiring knowledge... He is a real instructor!
от партнера 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.
от партнера 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.
от партнера 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!
от партнера AGAug 10, 2019
This course is not only very helpful for engineers but also helpful for under Graduate students.\n\nI like "Gram-schmidt orthogonalization process" based lecture.
от партнера JVApr 2, 2020
This is one of the important courses in engineering, it is highly recommended especially for those who want to excel their potential in calculations.
от партнера AAJan 10, 2019
Very systematic course ,not a typical first course in linear algebra but brilliant overall .Extremely useful for engineers.\n\nHighly recommended!!!
от партнера JSFeb 23, 2019
Yes, I spend 30 hours a week but I finished it in 2 weekends. Good course, a lot of video, going from the base to more complex subjects building up.
от партнера KCSep 14, 2019
I enjoyed doing all the exercises. Thank you for making the book available with the worked examples, which helped tremendously. Thank you Dr Chasnov
от партнера EMar 28, 2020
The videos were great but still, there are some topics that I still needed to find more videos from other sources in order to understand the topic.
от партнера GSNov 11, 2019
It was very detailed and gave a lot of important formulas for solving problems with Matrix algebra and the instructor followed a good pace.
от партнера VPFeb 20, 2019
A wonderful course for those who want to start Matrices from scratch. The course covers all the necessary things an engineer requires.
от партнера PPNov 5, 2019
excellent course. it helped me understand more about matrix algebra and its application. Thank you so much, Prof. Jeffrey R. Chasnov
от партнера HTJan 10, 2020
The course is really good . It is easy to learn and understand . I got a valuable knowledge of Matrix Algebra. Thank you so much !
от партнера JMJan 6, 2020
Incredible course, I highly recommend it to anyone in need of building up their math skills for engineering or even business.
от партнера LCMar 23, 2019
Good, but would have appreciated slides instead of just pdf, and tests are too much on manual calculus instead of thinking...
от партнера SAJul 9, 2019
Very clear and precise teaching material and videos. Concise explanations of the key ingredients of matrix algebra. Thanks.
от партнера ESDec 17, 2019
The course was very engaging and Jeffrey delivered it in a very simple way. I love it! Very recommended for the beginners.
от партнера ZBJan 23, 2020
A must-have course. Professor Chasnov is awesome. He is able to make it look simple. Only the best ones know this trick.
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