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110 classificações
27 avaliações

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Nível iniciante

Aprox. 14 horas para completar

Sugerido: 4 weeks of study, 3-4 hours/week...

Inglês

Legendas: Inglês

100% online

Comece imediatamente e aprenda em seu próprio cronograma.

Prazos flexíveis

Redefinir os prazos de acordo com sua programação.

Nível iniciante

Aprox. 14 horas para completar

Sugerido: 4 weeks of study, 3-4 hours/week...

Inglês

Legendas: Inglês

Programa - O que você aprenderá com este curso

Semana
1
7 horas para concluir

MATRICES

In this week's lectures, we learn about matrices. Matrices are rectangular arrays of numbers or other mathematical objects and are fundamental to engineering mathematics. We will 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. ...
11 vídeos (total de (Total 84 mín.) min), 24 leituras, 5 testes
11 videos
Introduction1min
Definition of a Matrix7min
Addition and Multiplication of Matrices10min
Special Matrices9min
Transpose Matrix9min
Inner and Outer Products9min
Inverse Matrix12min
Orthogonal Matrices4min
Rotation Matrices8min
Permutation Matrices6min
24 leituras
Welcome and Course Information5min
Get to Know Your Classmates10min
Practice: Construct Some Matrices10min
Practice: Matrix Addition and Multiplication10min
Practice: AB=AC Does Not Imply B=C10min
Practice: Matrix Multiplication Does Not Commute10min
Practice: AB=0 When A and B Are Not zero10min
Practice: Product of Diagonal Matrices10min
Practice: Product of Triangular Matrices10min
Practice: Transpose of a Matrix Product10min
Practice: Any Square Matrix Can Be Written as the Sum of a Symmetric and Skew-Symmetric Matrix10min
Practice: Construction of a Square Symmetric Matrix10min
Practice: Example of a Symmetric Matrix10min
Practice: Sum of the Squares of the Elements of a Matrix10min
Practice: Inverses of Two-by-Two Matrices10min
Practice: Inverse of a Matrix Product10min
Practice: Inverse of the Transpose Matrix10min
Practice: Uniqueness of the Inverse10min
Practice: Product of Orthogonal Matrices10min
Practice: The Identity Matrix is Orthogonal10min
Practice: Inverse of the Rotation Matrix10min
Practice: Three-dimensional Rotation10min
Practice: Three-by-Three Permutation Matrices10min
Practice: Inverses of Three-by-Three Permutation Matrices10min
5 exercícios práticos
Diagnostic Quiz10min
Matrix Definitions10min
Transposes and Inverses10min
Orthogonal Matrices10min
Week One30min
Semana
2
3 horas para concluir

SYSTEMS OF LINEAR EQUATIONS

In this week's lectures, we learn about solving a system of linear equations. A system of linear equations can be written in matrix form, and we can solve using Gaussian elimination. We will learn how to bring a matrix to reduced row echelon form, and how this can be used to compute a matrix inverse. We will also learn how to find the LU decomposition of a matrix, and how to use this decomposition to efficiently solve a system of linear equations....
7 vídeos (total de (Total 71 mín.) min), 6 leituras, 3 testes
7 videos
Gaussian Elimination14min
Reduced Row Echelon Form8min
Computing Inverses13min
Elementary Matrices11min
LU Decomposition10min
Solving (LU)x = b11min
6 leituras
Practice: Gaussian Elimination10min
Practice: Reduced Row Echelon Form10min
Practice: Computing Inverses10min
Practice: Elementary Matrices10min
Practice: LU Decomposition10min
Practice: Solving (LU)x = b10min
3 exercícios práticos
Gaussian Elimination10min
LU Decomposition10min
Week Two30min
Semana
3
6 horas para concluir

VECTOR SPACES

In this week's lectures, we learn about 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 will learn some of the vocabulary and phrases of linear algebra, such as linear independence, span, basis and dimension. We will 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....
13 vídeos (total de (Total 140 mín.) min), 14 leituras, 5 testes
13 videos
Vector Spaces7min
Linear Independence9min
Span, Basis and Dimension10min
Gram-Schmidt Process13min
Gram-Schmidt Process Example9min
Null Space12min
Application of the Null Space14min
Column Space9min
Row Space, Left Null Space and Rank14min
Orthogonal Projections11min
The Least-Squares Problem10min
Solution of the Least-Squares Problem15min
14 leituras
Practice: Zero Vector10min
Practice: Examples of Vector Spaces10min
Practice: Linear Independence10min
Practice: Orthonormal basis10min
Practice: Gram-Schmidt Process10min
Practice: Gram-Schmidt on Three-by-One Matrices10min
Practice: Gram-Schmidt on Four-by-One Matrices10min
Practice: Null Space10min
Practice: Underdetermined System of Linear Equations10min
Practice: Column Space10min
Practice: Fundamental Matrix Subspaces10min
Practice: Orthogonal Projections10min
Practice: Setting Up the Least-Squares Problem10min
Practice: Line of Best Fit10min
5 exercícios práticos
Vector Space Definitions10min
Gram-Schmidt Process10min
Fundamental Subspaces10min
Orthogonal Projections10min
Week Three30min
Semana
4
6 horas para concluir

EIGENVALUES AND EIGENVECTORS

In this week's lectures, we will learn about determinants and the eigenvalue problem. We will learn how to compute determinants using a Laplace expansion, the Leibniz formula, or by row or column elimination. We will formulate the eigenvalue problem and learn how to find the eigenvalues and eigenvectors of a matrix. We will 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. ...
13 vídeos (total de (Total 120 mín.) min), 20 leituras, 4 testes
13 videos
Two-by-Two and Three-by-Three Determinants8min
Laplace Expansion13min
Leibniz Formula11min
Properties of a Determinant15min
The Eigenvalue Problem12min
Finding Eigenvalues and Eigenvectors (1)10min
Finding Eigenvalues and Eigenvectors (2)7min
Matrix Diagonalization9min
Matrix Diagonalization Example15min
Powers of a Matrix5min
Powers of a Matrix Example6min
Concluding Remarks3min
20 leituras
Practice: Determinant of the Identity Matrix10min
Practice: Row Interchange10min
Practice: Determinant of a Matrix Product10min
Practice: Compute Determinant Using the Laplace Expansion10min
Practice: Compute Determinant Using the Leibniz Formula10min
Practice: Determinant of a Matrix With Two Equal Rows10min
Practice: Determinant is a Linear Function of Any Row10min
Practice: Determinant Can Be Computed Using Row Reduction10min
Practice: Compute Determinant Using Gaussian Elimination10min
Practice: Characteristic Equation for a Three-by-Three Matrix10min
Practice: Eigenvalues and Eigenvectors of a Two-by-Two Matrix10min
Practice: Eigenvalues and Eigenvectors of a Three-by-Three Matrix10min
Practice: Complex Eigenvalues10min
Practice: Linearly Independent Eigenvectors10min
Practice: Invertibility of the Eigenvector Matrix10min
Practice: Diagonalize a Three-by-Three Matrix10min
Practice: Matrix Exponential10min
Practice: Powers of a Matrix10min
Please Rate this Course10min
Acknowledgements1min
4 exercícios práticos
Determinants10min
The Eigenvalue Problem10min
Matrix Diagonalization10min
Week Four30min
4.8
27 avaliaçõesChevron Right

Melhores avaliações

por JMMar 12th 2019

Es muy bueno el curso de verdad que lo recomiendo mucho para todos aquellos estudiantes que cursan Álgebra Lineal ya que tiene todas las herramientas necesarias para aprender esa materia

por RHNov 7th 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.

Instrutores

Avatar

Jeffrey R. Chasnov

Professor
Department of Mathematics

Sobre 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....

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