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完成后获得证书
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可灵活调整截止日期
根据您的日程表重置截止日期。
初级
完成时间大约为20 小时
英语(English)
字幕:英语(English)

您将学到的内容有

  • Matrices

  • Systems of Linear Equations

  • Vector Spaces

  • Eigenvalues and eigenvectors

您将获得的技能

Linear AlgebraEngineering Mathematics

学生职业成果

50%

完成这些课程后已开始新的职业生涯

50%

通过此课程获得实实在在的工作福利
可分享的证书
完成后获得证书
100% 在线
立即开始,按照自己的计划学习。
可灵活调整截止日期
根据您的日程表重置截止日期。
初级
完成时间大约为20 小时
英语(English)
字幕:英语(English)

提供方

香港科技大学 徽标

香港科技大学

教学大纲 - 您将从这门课程中学到什么

内容评分Thumbs Up96%(4,161 个评分)Info
1

1

完成时间为 5 小时

MATRICES

完成时间为 5 小时
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 Matrix | Lecture 17分钟
Addition and Multiplication of Matrices | Lecture 210分钟
Special Matrices | Lecture 39分钟
Transpose Matrix | Lecture 49分钟
Inner and Outer Products | Lecture 59分钟
Inverse Matrix | Lecture 612分钟
Orthogonal Matrices | Lecture 74分钟
Rotation Matrices | Lecture 88分钟
Permutation Matrices | Lecture 96分钟
25 个阅读材料
Welcome and Course Information1分钟
How to Write Math in the Discussions Using MathJax1分钟
Construct Some Matrices5分钟
Matrix Addition and Multiplication5分钟
AB=AC Does Not Imply B=C5分钟
Matrix Multiplication Does Not Commute5分钟
Associative Law for Matrix Multiplication10分钟
AB=0 When A and B Are Not zero10分钟
Product of Diagonal Matrices5分钟
Product of Triangular Matrices10分钟
Transpose of a Matrix Product10分钟
Any Square Matrix Can Be Written as the Sum of a Symmetric and Skew-Symmetric Matrix5分钟
Construction of a Square Symmetric Matrix5分钟
Example of a Symmetric Matrix10分钟
Sum of the Squares of the Elements of a Matrix10分钟
Inverses of Two-by-Two Matrices5分钟
Inverse of a Matrix Product10分钟
Inverse of the Transpose Matrix10分钟
Uniqueness of the Inverse10分钟
Product of Orthogonal Matrices5分钟
The Identity Matrix is Orthogonal5分钟
Inverse of the Rotation Matrix5分钟
Three-dimensional Rotation10分钟
Three-by-Three Permutation Matrices10分钟
Inverses of Three-by-Three Permutation Matrices10分钟
5 个练习
Diagnostic Quiz5分钟
Matrix Definitions10分钟
Transposes and Inverses10分钟
Orthogonal Matrices10分钟
Week One Assessment30分钟
2

2

完成时间为 4 小时

SYSTEMS OF LINEAR EQUATIONS

完成时间为 4 小时
7 个视频 (总计 71 分钟), 6 个阅读材料, 3 个测验
7 个视频
Gaussian Elimination | Lecture 1014分钟
Reduced Row Echelon Form | Lecture 118分钟
Computing Inverses | Lecture 1213分钟
Elementary Matrices | Lecture 1311分钟
LU Decomposition | Lecture 1410分钟
Solving (LU)x = b | Lecture 1511分钟
6 个阅读材料
Gaussian Elimination15分钟
Reduced Row Echelon Form15分钟
Computing Inverses15分钟
Elementary Matrices5分钟
LU Decomposition15分钟
Solving (LU)x = b10分钟
3 个练习
Gaussian Elimination20分钟
LU Decomposition15分钟
Week Two Assessment30分钟
3

3

完成时间为 5 小时

VECTOR SPACES

完成时间为 5 小时
13 个视频 (总计 140 分钟), 14 个阅读材料, 5 个测验
13 个视频
Vector Spaces | Lecture 167分钟
Linear Independence | Lecture 179分钟
Span, Basis and Dimension | Lecture 1810分钟
Gram-Schmidt Process | Lecture 1913分钟
Gram-Schmidt Process Example | Lecture 209分钟
Null Space | Lecture 2112分钟
Application of the Null Space | Lecture 2214分钟
Column Space | Lecture 239分钟
Row Space, Left Null Space and Rank | Lecture 2414分钟
Orthogonal Projections | Lecture 2511分钟
The Least-Squares Problem | Lecture 2610分钟
Solution of the Least-Squares Problem | Lecture 2715分钟
14 个阅读材料
Zero Vector5分钟
Examples of Vector Spaces5分钟
Linear Independence5分钟
Orthonormal basis5分钟
Gram-Schmidt Process5分钟
Gram-Schmidt on Three-by-One Matrices5分钟
Gram-Schmidt on Four-by-One Matrices10分钟
Null Space10分钟
Underdetermined System of Linear Equations10分钟
Column Space5分钟
Fundamental Matrix Subspaces10分钟
Orthogonal Projections5分钟
Setting Up the Least-Squares Problem5分钟
Line of Best Fit5分钟
5 个练习
Vector Space Definitions15分钟
Gram-Schmidt Process15分钟
Fundamental Subspaces15分钟
Orthogonal Projections15分钟
Week Three Assessment30分钟
4

4

完成时间为 5 小时

EIGENVALUES AND EIGENVECTORS

完成时间为 5 小时
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 Determinants | Lecture 288分钟
Laplace Expansion | Lecture 2913分钟
Leibniz Formula | Lecture 3011分钟
Properties of a Determinant | Lecture 3115分钟
The Eigenvalue Problem | Lecture 3212分钟
Finding Eigenvalues and Eigenvectors (1) | Lecture 3310分钟
Finding Eigenvalues and Eigenvectors (2) | Lecture 347分钟
Matrix Diagonalization | Lecture 359分钟
Matrix Diagonalization Example | Lecture 3615分钟
Powers of a Matrix | Lecture 375分钟
Powers of a Matrix Example | Lecture 386分钟
Concluding Remarks3分钟
20 个阅读材料
Determinant of the Identity Matrix5分钟
Row Interchange5分钟
Determinant of a Matrix Product10分钟
Compute Determinant Using the Laplace Expansion5分钟
Compute Determinant Using the Leibniz Formula5分钟
Determinant of a Matrix With Two Equal Rows5分钟
Determinant is a Linear Function of Any Row5分钟
Determinant Can Be Computed Using Row Reduction5分钟
Compute Determinant Using Gaussian Elimination5分钟
Characteristic Equation for a Three-by-Three Matrix10分钟
Eigenvalues and Eigenvectors of a Two-by-Two Matrix5分钟
Eigenvalues and Eigenvectors of a Three-by-Three Matrix10分钟
Complex Eigenvalues5分钟
Linearly Independent Eigenvectors5分钟
Invertibility of the Eigenvector Matrix5分钟
Diagonalize a Three-by-Three Matrix10分钟
Matrix Exponential5分钟
Powers of a Matrix10分钟
Please Rate this Course1分钟
Acknowledgments
4 个练习
Determinants15分钟
The Eigenvalue Problem15分钟
Matrix Diagonalization15分钟
Week Four Assessment30分钟

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