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
Universidade de Ciência e Tecnologia de Hong KongInformações sobre o curso
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Prazos flexíveis
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Nível iniciante
Aprox. 20 horas para completar
Inglês
Legendas: Inglês
O que você vai aprender
Matrices
Systems of Linear Equations
Vector Spaces
Eigenvalues and eigenvectors
Habilidades que você terá
Linear AlgebraEngineering Mathematics
Resultados de carreira do aprendiz
50%
comecei uma nova carreira após concluir estes cursos
50%
consegui um benefício significativo de carreira com este curso
Certificados compartilháveis
Tenha o certificado após a conclusão
100% on-line
Comece imediatamente e aprenda em seu próprio cronograma.
Prazos flexíveis
Redefinir os prazos de acordo com sua programação.
Nível iniciante
Aprox. 20 horas para completar
Inglês
Legendas: Inglês
oferecido por
Universidade de Ciência e Tecnologia 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.
Programa - O que você aprenderá com este curso
5 horas para concluir
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 horas para concluir
11 vídeos (Total 84 mín.), 25 leituras, 5 testes
11 videos
Introduction1min
Definition of a Matrix | Lecture 17min
Addition and Multiplication of Matrices | Lecture 210min
Special Matrices | Lecture 39min
Transpose Matrix | Lecture 49min
Inner and Outer Products | Lecture 59min
Inverse Matrix | Lecture 612min
Orthogonal Matrices | Lecture 74min
Rotation Matrices | Lecture 88min
Permutation Matrices | Lecture 96min
25 leituras
Welcome and Course Information1min
How to Write Math in the Discussions Using MathJax1min
Construct Some Matrices5min
Matrix Addition and Multiplication5min
AB=AC Does Not Imply B=C5min
Matrix Multiplication Does Not Commute5min
Associative Law for Matrix Multiplication10min
AB=0 When A and B Are Not zero10min
Product of Diagonal Matrices5min
Product of Triangular Matrices10min
Transpose of a Matrix Product10min
Any Square Matrix Can Be Written as the Sum of a Symmetric and Skew-Symmetric Matrix5min
Construction of a Square Symmetric Matrix5min
Example of a Symmetric Matrix10min
Sum of the Squares of the Elements of a Matrix10min
Inverses of Two-by-Two Matrices5min
Inverse of a Matrix Product10min
Inverse of the Transpose Matrix10min
Uniqueness of the Inverse10min
Product of Orthogonal Matrices5min
The Identity Matrix is Orthogonal5min
Inverse of the Rotation Matrix5min
Three-dimensional Rotation10min
Three-by-Three Permutation Matrices10min
Inverses of Three-by-Three Permutation Matrices10min
5 exercícios práticos
Diagnostic Quiz5min
Matrix Definitions10min
Transposes and Inverses10min
Orthogonal Matrices10min
Week One Assessment30min
4 horas para concluir
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 horas para concluir
7 vídeos (Total 71 mín.), 6 leituras, 3 testes
7 videos
Introduction1min
Gaussian Elimination | Lecture 1014min
Reduced Row Echelon Form | Lecture 118min
Computing Inverses | Lecture 1213min
Elementary Matrices | Lecture 1311min
LU Decomposition | Lecture 1410min
Solving (LU)x = b | Lecture 1511min
6 leituras
Gaussian Elimination15min
Reduced Row Echelon Form15min
Computing Inverses15min
Elementary Matrices5min
LU Decomposition15min
Solving (LU)x = b10min
3 exercícios práticos
Gaussian Elimination20min
LU Decomposition15min
Week Two Assessment30min
5 horas para concluir
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 horas para concluir
13 vídeos (Total 140 mín.), 14 leituras, 5 testes
13 videos
Introduction1min
Vector Spaces | Lecture 167min
Linear Independence | Lecture 179min
Span, Basis and Dimension | Lecture 1810min
Gram-Schmidt Process | Lecture 1913min
Gram-Schmidt Process Example | Lecture 209min
Null Space | Lecture 2112min
Application of the Null Space | Lecture 2214min
Column Space | Lecture 239min
Row Space, Left Null Space and Rank | Lecture 2414min
Orthogonal Projections | Lecture 2511min
The Least-Squares Problem | Lecture 2610min
Solution of the Least-Squares Problem | Lecture 2715min
14 leituras
Zero Vector5min
Examples of Vector Spaces5min
Linear Independence5min
Orthonormal basis5min
Gram-Schmidt Process5min
Gram-Schmidt on Three-by-One Matrices5min
Gram-Schmidt on Four-by-One Matrices10min
Null Space10min
Underdetermined System of Linear Equations10min
Column Space5min
Fundamental Matrix Subspaces10min
Orthogonal Projections5min
Setting Up the Least-Squares Problem5min
Line of Best Fit5min
5 exercícios práticos
Vector Space Definitions15min
Gram-Schmidt Process15min
Fundamental Subspaces15min
Orthogonal Projections15min
Week Three Assessment30min
5 horas para concluir
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 horas para concluir
13 vídeos (Total 120 mín.), 20 leituras, 4 testes
13 videos
Introduction1min
Two-by-Two and Three-by-Three Determinants | Lecture 288min
Laplace Expansion | Lecture 2913min
Leibniz Formula | Lecture 3011min
Properties of a Determinant | Lecture 3115min
The Eigenvalue Problem | Lecture 3212min
Finding Eigenvalues and Eigenvectors (1) | Lecture 3310min
Finding Eigenvalues and Eigenvectors (2) | Lecture 347min
Matrix Diagonalization | Lecture 359min
Matrix Diagonalization Example | Lecture 3615min
Powers of a Matrix | Lecture 375min
Powers of a Matrix Example | Lecture 386min
Concluding Remarks3min
20 leituras
Determinant of the Identity Matrix5min
Row Interchange5min
Determinant of a Matrix Product10min
Compute Determinant Using the Laplace Expansion5min
Compute Determinant Using the Leibniz Formula5min
Determinant of a Matrix With Two Equal Rows5min
Determinant is a Linear Function of Any Row5min
Determinant Can Be Computed Using Row Reduction5min
Compute Determinant Using Gaussian Elimination5min
Characteristic Equation for a Three-by-Three Matrix10min
Eigenvalues and Eigenvectors of a Two-by-Two Matrix5min
Eigenvalues and Eigenvectors of a Three-by-Three Matrix10min
Complex Eigenvalues5min
Linearly Independent Eigenvectors5min
Invertibility of the Eigenvector Matrix5min
Diagonalize a Three-by-Three Matrix10min
Matrix Exponential5min
Powers of a Matrix10min
Please Rate this Course1min
Acknowledgments
4 exercícios práticos
Determinants15min
The Eigenvalue Problem15min
Matrix Diagonalization15min
Week Four Assessment30min
Avaliações
Principais avaliações do MATRIX ALGEBRA FOR ENGINEERS
por RH6 de Nov de 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.
por DL30 de Abr de 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.
por RZ5 de Out de 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.
por CG2 de Mar de 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!
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