Mathematical Matrix Methods lie at the root of most methods of machine learning and data analysis of tabular data. Learn the basics of Matrix Methods, including matrix-matrix multiplication, solving linear equations, orthogonality, and best least squares approximation. Discover the Singular Value Decomposition that plays a fundamental role in dimensionality reduction, Principal Component Analysis, and noise reduction. Optional examples using Python are used to illustrate the concepts and allow the learner to experiment with the algorithms.
课程信息
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教学大纲 - 您将从这门课程中学到什么
周
1完成时间为 1 小时
Matrices as Mathematical Objects
3 个视频 （总计 11 分钟）, 2 个阅读材料, 3 个测验
2 个阅读材料
Vector and Matrix operations30分钟
Matrix Multiplication10分钟
3 个练习
Matrix8分钟
Linear combinations
Matrix Combinations
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2完成时间为 1 小时
Matrix Multiplication and other Operations
3 个视频 （总计 14 分钟）, 2 个阅读材料, 3 个测验
2 个阅读材料
Matrix Arithmetic10分钟
Matrix Transpose10分钟
3 个练习
Matrix Operations4分钟
Matrix Transpose4分钟
Matrix Multiplication and Other Operations
周
3完成时间为 1 小时
Systems of Linear Equations
4 个视频 （总计 15 分钟）, 3 个阅读材料, 4 个测验
4 个视频
Solution of Linear Equations via Elimination2分钟
LU Decomposition: Matrix is a Product of Simple Matrices5分钟
Supplement: Solve Linear Equations in Python2分钟
3 个阅读材料
Systems of Linear Equations10分钟
Gaussian Elimination Algorithm10分钟
LU Decomposition10分钟
4 个练习
Systems of Linear Equations
Solution of Linear Equations via Elimination
LU Decomposition
Systems of linear equations
周
4完成时间为 1 小时
Linear Least Squares
4 个视频 （总计 16 分钟）, 2 个阅读材料, 5 个测验
4 个视频
Linear Least Squares: Best Approximation3分钟
Least Distance -> Orthogonality -> Normal Equations4分钟
Example: Approximate Curve Fitting4分钟
2 个阅读材料
Orthogonality and the Inner Product10分钟
Linear Least Squares10分钟
5 个练习
Orthogonality and Inner Product
Linear Least Squares
Normal equations4分钟
Approximate Curve Fitting4分钟
Linear Least Squares
讲师
Daniel Boley
ProfessorComputer Science and Engineering
关于 明尼苏达大学
The University of Minnesota is among the largest public research universities in the country, offering undergraduate, graduate, and professional students a multitude of opportunities for study and research. Located at the heart of one of the nation’s most vibrant, diverse metropolitan communities, students on the campuses in Minneapolis and St. Paul benefit from extensive partnerships with world-renowned health centers, international corporations, government agencies, and arts, nonprofit, and public service organizations.
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