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
Université des sciences et technologies de Hong Kong
À propos de ce cours
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Résultats de carrière des étudiants
50%
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Ce que vous allez apprendre
Matrices
Systems of Linear Equations
Vector Spaces
Eigenvalues and eigenvectors
Compétences que vous acquerrez
Linear AlgebraEngineering Mathematics
Résultats de carrière des étudiants
50%
ont commencé une nouvelle carrière après avoir terminé ce cours
50%
ont bénéficié d'un avantage concret dans leur carrières grâce à ce cours
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Dates limites flexibles
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Niveau débutant
Approx. 14 heures pour terminer
Recommandé : 4 weeks of study, 4-5 hours/week
Anglais
Sous-titres : Anglais
Offert par
Université des sciences et technologies de Hong Kong
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.
Programme du cours : ce que vous apprendrez dans ce cours
5 heures pour terminer
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 heures pour terminer
11 vidéos (Total 84 min), 25 lectures, 5 quiz
11 vidéos
Promotional Video4 min
Introduction1 min
Definition of a Matrix | Lecture 17 min
Addition and Multiplication of Matrices | Lecture 210 min
Special Matrices | Lecture 39 min
Transpose Matrix | Lecture 49 min
Inner and Outer Products | Lecture 59 min
Inverse Matrix | Lecture 612 min
Orthogonal Matrices | Lecture 74 min
Rotation Matrices | Lecture 88 min
Permutation Matrices | Lecture 96 min
25 lectures
Welcome and Course Information1 min
How to Write Math in the Discussions Using MathJax1 min
Construct Some Matrices5 min
Matrix Addition and Multiplication5 min
AB=AC Does Not Imply B=C5 min
Matrix Multiplication Does Not Commute5 min
Associative Law for Matrix Multiplication10 min
AB=0 When A and B Are Not zero10 min
Product of Diagonal Matrices5 min
Product of Triangular Matrices10 min
Transpose of a Matrix Product10 min
Any Square Matrix Can Be Written as the Sum of a Symmetric and Skew-Symmetric Matrix5 min
Construction of a Square Symmetric Matrix5 min
Example of a Symmetric Matrix10 min
Sum of the Squares of the Elements of a Matrix10 min
Inverses of Two-by-Two Matrices5 min
Inverse of a Matrix Product10 min
Inverse of the Transpose Matrix10 min
Uniqueness of the Inverse10 min
Product of Orthogonal Matrices5 min
The Identity Matrix is Orthogonal5 min
Inverse of the Rotation Matrix5 min
Three-dimensional Rotation10 min
Three-by-Three Permutation Matrices10 min
Inverses of Three-by-Three Permutation Matrices10 min
5 exercices pour s'entraîner
Diagnostic Quiz5 min
Matrix Definitions10 min
Transposes and Inverses10 min
Orthogonal Matrices10 min
Week One Assessment30 min
4 heures pour terminer
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 heures pour terminer
7 vidéos (Total 71 min), 6 lectures, 3 quiz
7 vidéos
Introduction1 min
Gaussian Elimination | Lecture 1014 min
Reduced Row Echelon Form | Lecture 118 min
Computing Inverses | Lecture 1213 min
Elementary Matrices | Lecture 1311 min
LU Decomposition | Lecture 1410 min
Solving (LU)x = b | Lecture 1511 min
6 lectures
Gaussian Elimination15 min
Reduced Row Echelon Form15 min
Computing Inverses15 min
Elementary Matrices5 min
LU Decomposition15 min
Solving (LU)x = b10 min
3 exercices pour s'entraîner
Gaussian Elimination20 min
LU Decomposition15 min
Week Two Assessment30 min
5 heures pour terminer
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 heures pour terminer
13 vidéos (Total 140 min), 14 lectures, 5 quiz
13 vidéos
Introduction1 min
Vector Spaces | Lecture 167 min
Linear Independence | Lecture 179 min
Span, Basis and Dimension | Lecture 1810 min
Gram-Schmidt Process | Lecture 1913 min
Gram-Schmidt Process Example | Lecture 209 min
Null Space | Lecture 2112 min
Application of the Null Space | Lecture 2214 min
Column Space | Lecture 239 min
Row Space, Left Null Space and Rank | Lecture 2414 min
Orthogonal Projections | Lecture 2511 min
The Least-Squares Problem | Lecture 2610 min
Solution of the Least-Squares Problem | Lecture 2715 min
14 lectures
Zero Vector5 min
Examples of Vector Spaces5 min
Linear Independence5 min
Orthonormal basis5 min
Gram-Schmidt Process5 min
Gram-Schmidt on Three-by-One Matrices5 min
Gram-Schmidt on Four-by-One Matrices10 min
Null Space10 min
Underdetermined System of Linear Equations10 min
Column Space5 min
Fundamental Matrix Subspaces10 min
Orthogonal Projections5 min
Setting Up the Least-Squares Problem5 min
Line of Best Fit5 min
5 exercices pour s'entraîner
Vector Space Definitions15 min
Gram-Schmidt Process15 min
Fundamental Subspaces15 min
Orthogonal Projections15 min
Week Three Assessment30 min
5 heures pour terminer
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 heures pour terminer
13 vidéos (Total 120 min), 20 lectures, 4 quiz
13 vidéos
Introduction1 min
Two-by-Two and Three-by-Three Determinants | Lecture 288 min
Laplace Expansion | Lecture 2913 min
Leibniz Formula | Lecture 3011 min
Properties of a Determinant | Lecture 3115 min
The Eigenvalue Problem | Lecture 3212 min
Finding Eigenvalues and Eigenvectors (1) | Lecture 3310 min
Finding Eigenvalues and Eigenvectors (2) | Lecture 347 min
Matrix Diagonalization | Lecture 359 min
Matrix Diagonalization Example | Lecture 3615 min
Powers of a Matrix | Lecture 375 min
Powers of a Matrix Example | Lecture 386 min
Concluding Remarks3 min
20 lectures
Determinant of the Identity Matrix5 min
Row Interchange5 min
Determinant of a Matrix Product10 min
Compute Determinant Using the Laplace Expansion5 min
Compute Determinant Using the Leibniz Formula5 min
Determinant of a Matrix With Two Equal Rows5 min
Determinant is a Linear Function of Any Row5 min
Determinant Can Be Computed Using Row Reduction5 min
Compute Determinant Using Gaussian Elimination5 min
Characteristic Equation for a Three-by-Three Matrix10 min
Eigenvalues and Eigenvectors of a Two-by-Two Matrix5 min
Eigenvalues and Eigenvectors of a Three-by-Three Matrix10 min
Complex Eigenvalues5 min
Linearly Independent Eigenvectors5 min
Invertibility of the Eigenvector Matrix5 min
Diagonalize a Three-by-Three Matrix10 min
Matrix Exponential5 min
Powers of a Matrix10 min
Please Rate this Course1 min
Acknowledgments
4 exercices pour s'entraîner
Determinants15 min
The Eigenvalue Problem15 min
Matrix Diagonalization15 min
Week Four Assessment30 min
Avis
4.8
Meilleurs avis pour MATRIX ALGEBRA FOR ENGINEERS
par 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.
par 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!
par 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.
par 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.
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