4.8
157 个评分
40 个审阅

1

## 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 个视频 （总计 84 分钟）, 25 个阅读材料, 5 个测验
11 个视频
Introduction1分钟
Definition of a Matrix7分钟
Special Matrices9分钟
Transpose Matrix9分钟
Inner and Outer Products9分钟
Inverse Matrix12分钟
Orthogonal Matrices4分钟
Rotation Matrices8分钟
Permutation Matrices6分钟
25 个阅读材料
Welcome and Course Information5分钟
Practice: Construct Some Matrices10分钟
Practice: AB=AC Does Not Imply B=C10分钟
Practice: Matrix Multiplication Does Not Commute10分钟
Practice: Associative Law for Matrix Multiplication10分钟
Practice: AB=0 When A and B Are Not zero10分钟
Practice: Product of Diagonal Matrices10分钟
Practice: Product of Triangular Matrices10分钟
Practice: Transpose of a Matrix Product10分钟
Practice: Any Square Matrix Can Be Written as the Sum of a Symmetric and Skew-Symmetric Matrix10分钟
Practice: Construction of a Square Symmetric Matrix10分钟
Practice: Example of a Symmetric Matrix10分钟
Practice: Sum of the Squares of the Elements of a Matrix10分钟
Practice: Inverses of Two-by-Two Matrices10分钟
Practice: Inverse of a Matrix Product10分钟
Practice: Inverse of the Transpose Matrix10分钟
Practice: Uniqueness of the Inverse10分钟
Practice: Product of Orthogonal Matrices10分钟
Practice: The Identity Matrix is Orthogonal10分钟
Practice: Inverse of the Rotation Matrix10分钟
Practice: Three-dimensional Rotation10分钟
Practice: Three-by-Three Permutation Matrices10分钟
Practice: Inverses of Three-by-Three Permutation Matrices10分钟
5 个练习
Diagnostic Quiz10分钟
Matrix Definitions10分钟
Transposes and Inverses10分钟
Orthogonal Matrices10分钟
Week One30分钟
2

## 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 个视频 （总计 71 分钟）, 6 个阅读材料, 3 个测验
7 个视频
Gaussian Elimination14分钟
Reduced Row Echelon Form8分钟
Computing Inverses13分钟
Elementary Matrices11分钟
LU Decomposition10分钟
Solving (LU)x = b11分钟
6 个阅读材料
Practice: Gaussian Elimination10分钟
Practice: Reduced Row Echelon Form10分钟
Practice: Computing Inverses10分钟
Practice: Elementary Matrices10分钟
Practice: LU Decomposition10分钟
Practice: Solving (LU)x = b10分钟
3 个练习
Gaussian Elimination10分钟
LU Decomposition10分钟
Week Two30分钟
3

## 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 个视频 （总计 140 分钟）, 14 个阅读材料, 5 个测验
13 个视频
Vector Spaces7分钟
Linear Independence9分钟
Span, Basis and Dimension10分钟
Gram-Schmidt Process13分钟
Gram-Schmidt Process Example9分钟
Null Space12分钟
Application of the Null Space14分钟
Column Space9分钟
Row Space, Left Null Space and Rank14分钟
Orthogonal Projections11分钟
The Least-Squares Problem10分钟
Solution of the Least-Squares Problem15分钟
14 个阅读材料
Practice: Zero Vector10分钟
Practice: Examples of Vector Spaces10分钟
Practice: Linear Independence10分钟
Practice: Orthonormal basis10分钟
Practice: Gram-Schmidt Process10分钟
Practice: Gram-Schmidt on Three-by-One Matrices10分钟
Practice: Gram-Schmidt on Four-by-One Matrices10分钟
Practice: Null Space10分钟
Practice: Underdetermined System of Linear Equations10分钟
Practice: Column Space10分钟
Practice: Fundamental Matrix Subspaces10分钟
Practice: Orthogonal Projections10分钟
Practice: Setting Up the Least-Squares Problem10分钟
Practice: Line of Best Fit10分钟
5 个练习
Vector Space Definitions10分钟
Gram-Schmidt Process10分钟
Fundamental Subspaces10分钟
Orthogonal Projections10分钟
Week Three30分钟
4

## 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 个视频 （总计 120 分钟）, 20 个阅读材料, 4 个测验
13 个视频
Two-by-Two and Three-by-Three Determinants8分钟
Laplace Expansion13分钟
Leibniz Formula11分钟
Properties of a Determinant15分钟
The Eigenvalue Problem12分钟
Finding Eigenvalues and Eigenvectors (1)10分钟
Finding Eigenvalues and Eigenvectors (2)7分钟
Matrix Diagonalization9分钟
Matrix Diagonalization Example15分钟
Powers of a Matrix5分钟
Powers of a Matrix Example6分钟
Concluding Remarks3分钟
20 个阅读材料
Practice: Determinant of the Identity Matrix10分钟
Practice: Row Interchange10分钟
Practice: Determinant of a Matrix Product10分钟
Practice: Compute Determinant Using the Laplace Expansion10分钟
Practice: Compute Determinant Using the Leibniz Formula10分钟
Practice: Determinant of a Matrix With Two Equal Rows10分钟
Practice: Determinant is a Linear Function of Any Row10分钟
Practice: Determinant Can Be Computed Using Row Reduction10分钟
Practice: Compute Determinant Using Gaussian Elimination10分钟
Practice: Characteristic Equation for a Three-by-Three Matrix10分钟
Practice: Eigenvalues and Eigenvectors of a Two-by-Two Matrix10分钟
Practice: Eigenvalues and Eigenvectors of a Three-by-Three Matrix10分钟
Practice: Complex Eigenvalues10分钟
Practice: Linearly Independent Eigenvectors10分钟
Practice: Invertibility of the Eigenvector Matrix10分钟
Practice: Diagonalize a Three-by-Three Matrix10分钟
Practice: Matrix Exponential10分钟
Practice: Powers of a Matrix10分钟
Acknowledgements1分钟
4 个练习
Determinants10分钟
The Eigenvalue Problem10分钟
Matrix Diagonalization10分钟
Week Four30分钟
4.8
40 个审阅

## 50%

### 热门审阅

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

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.

## 讲师

### Jeffrey R. Chasnov

Professor
Department of Mathematics

## 关于 香港科技大学

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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