36,704 次近期查看

### 您將學到的內容有

• Matrices

• Systems of Linear Equations

• Vector Spaces

• Eigenvalues and eigenvectors

### 您將獲得的技能

Eigenvalues And EigenvectorsGaussian EliminationEngineering MathematicsMatricesLinear Algebra

1

## MATRICES

11 個視頻 （總計 84 分鐘）, 26 個閱讀材料, 5 個測驗
11 個視頻
Introduction1分鐘
Definition of a Matrix7分鐘
Special Matrices9分鐘
Transpose Matrix9分鐘
Inner and Outer Products9分鐘
Inverse Matrix12分鐘
Orthogonal Matrices4分鐘
Rotation Matrices8分鐘
Permutation Matrices6分鐘
26 個閱讀材料
Welcome and Course Information1分鐘
How to Write Math in the Discussions Using MathJax1分鐘
Practice: Construct Some Matrices5分鐘
Practice: AB=AC Does Not Imply B=C5分鐘
Practice: Matrix Multiplication Does Not Commute5分鐘
Practice: Associative Law for Matrix Multiplication5分鐘
Practice: AB=0 When A and B Are Not zero5分鐘
Practice: Product of Diagonal Matrices5分鐘
Practice: Product of Triangular Matrices5分鐘
Practice: Transpose of a Matrix Product5分鐘
Practice: Any Square Matrix Can Be Written as the Sum of a Symmetric and Skew-Symmetric Matrix5分鐘
Practice: Construction of a Square Symmetric Matrix5分鐘
Practice: Example of a Symmetric Matrix5分鐘
Practice: Sum of the Squares of the Elements of a Matrix5分鐘
Practice: Inverses of Two-by-Two Matrices5分鐘
Practice: Inverse of a Matrix Product5分鐘
Practice: Inverse of the Transpose Matrix5分鐘
Practice: Uniqueness of the Inverse5分鐘
Practice: Product of Orthogonal Matrices5分鐘
Practice: The Identity Matrix is Orthogonal5分鐘
Practice: Inverse of the Rotation Matrix5分鐘
Practice: Three-dimensional Rotation5分鐘
Practice: Three-by-Three Permutation Matrices5分鐘
Practice: Inverses of Three-by-Three Permutation Matrices5分鐘
5 個練習
Diagnostic Quiz5分鐘
Matrix Definitions10分鐘
Transposes and Inverses10分鐘
Orthogonal Matrices10分鐘
Week One30分鐘
2

## SYSTEMS OF LINEAR EQUATIONS

7 個視頻 （總計 71 分鐘）, 6 個閱讀材料, 3 個測驗
7 個視頻
Gaussian Elimination14分鐘
Reduced Row Echelon Form8分鐘
Computing Inverses13分鐘
Elementary Matrices11分鐘
LU Decomposition10分鐘
Solving (LU)x = b11分鐘
6 個閱讀材料
Practice: Gaussian Elimination5分鐘
Practice: Reduced Row Echelon Form5分鐘
Practice: Computing Inverses5分鐘
Practice: Elementary Matrices5分鐘
Practice: LU Decomposition5分鐘
Practice: Solving (LU)x = b5分鐘
3 個練習
Gaussian Elimination15分鐘
LU Decomposition15分鐘
Week Two30分鐘
3

## VECTOR SPACES

13 個視頻 （總計 140 分鐘）, 14 個閱讀材料, 5 個測驗
13 個視頻
Vector Spaces7分鐘
Linear Independence9分鐘
Span, Basis and Dimension10分鐘
Gram-Schmidt Process13分鐘
Gram-Schmidt Process Example9分鐘
Null Space12分鐘
Application of the Null Space14分鐘
Column Space9分鐘
Row Space, Left Null Space and Rank14分鐘
Orthogonal Projections11分鐘
The Least-Squares Problem10分鐘
Solution of the Least-Squares Problem15分鐘
14 個閱讀材料
Practice: Zero Vector5分鐘
Practice: Examples of Vector Spaces5分鐘
Practice: Linear Independence5分鐘
Practice: Orthonormal basis5分鐘
Practice: Gram-Schmidt Process5分鐘
Practice: Gram-Schmidt on Three-by-One Matrices5分鐘
Practice: Gram-Schmidt on Four-by-One Matrices5分鐘
Practice: Null Space5分鐘
Practice: Underdetermined System of Linear Equations5分鐘
Practice: Column Space5分鐘
Practice: Fundamental Matrix Subspaces5分鐘
Practice: Orthogonal Projections5分鐘
Practice: Setting Up the Least-Squares Problem5分鐘
Practice: Line of Best Fit5分鐘
5 個練習
Vector Space Definitions15分鐘
Gram-Schmidt Process15分鐘
Fundamental Subspaces15分鐘
Orthogonal Projections15分鐘
Week Three30分鐘
4

## EIGENVALUES AND EIGENVECTORS

13 個視頻 （總計 120 分鐘）, 20 個閱讀材料, 4 個測驗
13 個視頻
Two-by-Two and Three-by-Three Determinants8分鐘
Laplace Expansion13分鐘
Leibniz Formula11分鐘
Properties of a Determinant15分鐘
The Eigenvalue Problem12分鐘
Finding Eigenvalues and Eigenvectors (1)10分鐘
Finding Eigenvalues and Eigenvectors (2)7分鐘
Matrix Diagonalization9分鐘
Matrix Diagonalization Example15分鐘
Powers of a Matrix5分鐘
Powers of a Matrix Example6分鐘
Concluding Remarks3分鐘
20 個閱讀材料
Practice: Determinant of the Identity Matrix5分鐘
Practice: Row Interchange5分鐘
Practice: Determinant of a Matrix Product5分鐘
Practice: Compute Determinant Using the Laplace Expansion5分鐘
Practice: Compute Determinant Using the Leibniz Formula5分鐘
Practice: Determinant of a Matrix With Two Equal Rows5分鐘
Practice: Determinant is a Linear Function of Any Row5分鐘
Practice: Determinant Can Be Computed Using Row Reduction5分鐘
Practice: Compute Determinant Using Gaussian Elimination5分鐘
Practice: Characteristic Equation for a Three-by-Three Matrix5分鐘
Practice: Eigenvalues and Eigenvectors of a Two-by-Two Matrix5分鐘
Practice: Eigenvalues and Eigenvectors of a Three-by-Three Matrix5分鐘
Practice: Complex Eigenvalues5分鐘
Practice: Linearly Independent Eigenvectors5分鐘
Practice: Invertibility of the Eigenvector Matrix5分鐘
Practice: Diagonalize a Three-by-Three Matrix5分鐘
Practice: Matrix Exponential5分鐘
Practice: Powers of a Matrix5分鐘
Acknowledgments
4 個練習
Determinants15分鐘
The Eigenvalue Problem15分鐘
Matrix Diagonalization15分鐘
Week Four30分鐘
4.8
83 條評論

## 50%

### 來自Matrix Algebra for Engineers的熱門評論

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.

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!

## 講師

### Jeffrey R. Chasnov

Professor
Department of Mathematics

## 關於 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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