# 課程信息

40,557 次近期查看

## 50%

### 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

Linear AlgebraEngineering Mathematics

1

# MATRICES

11 個視頻 （總計 84 分鐘）, 25 個閱讀材料, 5 個測驗
11 個視頻
Introduction1分鐘
Definition of a Matrix | Lecture 17分鐘
Addition and Multiplication of Matrices | Lecture 210分鐘
Special Matrices | Lecture 39分鐘
Transpose Matrix | Lecture 49分鐘
Inner and Outer Products | Lecture 59分鐘
Inverse Matrix | Lecture 612分鐘
Orthogonal Matrices | Lecture 74分鐘
Rotation Matrices | Lecture 88分鐘
Permutation Matrices | Lecture 96分鐘
25 個閱讀材料
Welcome and Course Information1分鐘
How to Write Math in the Discussions Using MathJax1分鐘
Construct Some Matrices5分鐘
AB=AC Does Not Imply B=C5分鐘
Matrix Multiplication Does Not Commute5分鐘
Associative Law for Matrix Multiplication10分鐘
AB=0 When A and B Are Not zero10分鐘
Product of Diagonal Matrices5分鐘
Product of Triangular Matrices10分鐘
Transpose of a Matrix Product10分鐘
Any Square Matrix Can Be Written as the Sum of a Symmetric and Skew-Symmetric Matrix5分鐘
Construction of a Square Symmetric Matrix5分鐘
Example of a Symmetric Matrix10分鐘
Sum of the Squares of the Elements of a Matrix10分鐘
Inverses of Two-by-Two Matrices5分鐘
Inverse of a Matrix Product10分鐘
Inverse of the Transpose Matrix10分鐘
Uniqueness of the Inverse10分鐘
Product of Orthogonal Matrices5分鐘
The Identity Matrix is Orthogonal5分鐘
Inverse of the Rotation Matrix5分鐘
Three-dimensional Rotation10分鐘
Three-by-Three Permutation Matrices10分鐘
Inverses of Three-by-Three Permutation Matrices10分鐘
5 個練習
Diagnostic Quiz5分鐘
Matrix Definitions10分鐘
Transposes and Inverses10分鐘
Orthogonal Matrices10分鐘
Week One Assessment30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 Elimination | Lecture 1014分鐘
Reduced Row Echelon Form | Lecture 118分鐘
Computing Inverses | Lecture 1213分鐘
Elementary Matrices | Lecture 1311分鐘
LU Decomposition | Lecture 1410分鐘
Solving (LU)x = b | Lecture 1511分鐘
6 個閱讀材料
Gaussian Elimination15分鐘
Reduced Row Echelon Form15分鐘
Computing Inverses15分鐘
Elementary Matrices5分鐘
LU Decomposition15分鐘
Solving (LU)x = b10分鐘
3 個練習
Gaussian Elimination20分鐘
LU Decomposition15分鐘
Week Two Assessment30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 Spaces | Lecture 167分鐘
Linear Independence | Lecture 179分鐘
Span, Basis and Dimension | Lecture 1810分鐘
Gram-Schmidt Process | Lecture 1913分鐘
Gram-Schmidt Process Example | Lecture 209分鐘
Null Space | Lecture 2112分鐘
Application of the Null Space | Lecture 2214分鐘
Column Space | Lecture 239分鐘
Row Space, Left Null Space and Rank | Lecture 2414分鐘
Orthogonal Projections | Lecture 2511分鐘
The Least-Squares Problem | Lecture 2610分鐘
Solution of the Least-Squares Problem | Lecture 2715分鐘
14 個閱讀材料
Zero Vector5分鐘
Examples of Vector Spaces5分鐘
Linear Independence5分鐘
Orthonormal basis5分鐘
Gram-Schmidt Process5分鐘
Gram-Schmidt on Three-by-One Matrices5分鐘
Gram-Schmidt on Four-by-One Matrices10分鐘
Null Space10分鐘
Underdetermined System of Linear Equations10分鐘
Column Space5分鐘
Fundamental Matrix Subspaces10分鐘
Orthogonal Projections5分鐘
Setting Up the Least-Squares Problem5分鐘
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 Three Assessment30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 Determinants | Lecture 288分鐘
Laplace Expansion | Lecture 2913分鐘
Leibniz Formula | Lecture 3011分鐘
Properties of a Determinant | Lecture 3115分鐘
The Eigenvalue Problem | Lecture 3212分鐘
Finding Eigenvalues and Eigenvectors (1) | Lecture 3310分鐘
Finding Eigenvalues and Eigenvectors (2) | Lecture 347分鐘
Matrix Diagonalization | Lecture 359分鐘
Matrix Diagonalization Example | Lecture 3615分鐘
Powers of a Matrix | Lecture 375分鐘
Powers of a Matrix Example | Lecture 386分鐘
Concluding Remarks3分鐘
20 個閱讀材料
Determinant of the Identity Matrix5分鐘
Row Interchange5分鐘
Determinant of a Matrix Product10分鐘
Compute Determinant Using the Laplace Expansion5分鐘
Compute Determinant Using the Leibniz Formula5分鐘
Determinant of a Matrix With Two Equal Rows5分鐘
Determinant is a Linear Function of Any Row5分鐘
Determinant Can Be Computed Using Row Reduction5分鐘
Compute Determinant Using Gaussian Elimination5分鐘
Characteristic Equation for a Three-by-Three Matrix10分鐘
Eigenvalues and Eigenvectors of a Two-by-Two Matrix5分鐘
Eigenvalues and Eigenvectors of a Three-by-Three Matrix10分鐘
Complex Eigenvalues5分鐘
Linearly Independent Eigenvectors5分鐘
Invertibility of the Eigenvector Matrix5分鐘
Diagonalize a Three-by-Three Matrix10分鐘
Matrix Exponential5分鐘
Powers of a Matrix10分鐘
Acknowledgments
4 個練習
Determinants15分鐘
The Eigenvalue Problem15分鐘
Matrix Diagonalization15分鐘
Week Four Assessment30分鐘
4.8

# 96 條評論

### 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.

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.

### 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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