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.
教學大綱 - 您將從這門課程中學到什麼
週
1完成時間為 1 小時
Matrices as Mathematical Objects
3 個視頻 （總計 11 分鐘）, 2 個閱讀材料, 3 個測驗
2 個閱讀材料
Vector and Matrix operations30分鐘
Matrix Multiplication10分鐘
3 個練習
Matrix8分鐘
Linear combinations
Matrix Combinations
週
2完成時間為 1 小時
Matrix Multiplication and other Operations
3 個視頻 （總計 14 分鐘）, 2 個閱讀材料, 3 個測驗
2 個閱讀材料
Matrix Arithmetic10分鐘
Matrix Transpose10分鐘
3 個練習
Matrix Operations4分鐘
Matrix Transpose4分鐘
Matrix Multiplication and Other Operations
週
3完成時間為 1 小時
Systems of Linear Equations
4 個視頻 （總計 15 分鐘）, 3 個閱讀材料, 4 個測驗
4 個視頻
Solution of Linear Equations via Elimination2分鐘
LU Decomposition: Matrix is a Product of Simple Matrices5分鐘
Supplement: Solve Linear Equations in Python2分鐘
3 個閱讀材料
Systems of Linear Equations10分鐘
Gaussian Elimination Algorithm10分鐘
LU Decomposition10分鐘
4 個練習
Systems of Linear Equations
Solution of Linear Equations via Elimination
LU Decomposition
Systems of linear equations
週
4完成時間為 1 小時
Linear Least Squares
4 個視頻 （總計 16 分鐘）, 2 個閱讀材料, 5 個測驗
4 個視頻
Linear Least Squares: Best Approximation3分鐘
Least Distance -> Orthogonality -> Normal Equations4分鐘
Example: Approximate Curve Fitting4分鐘
2 個閱讀材料
Orthogonality and the Inner Product10分鐘
Linear Least Squares10分鐘
5 個練習
Orthogonality and Inner Product
Linear Least Squares
Normal equations4分鐘
Approximate Curve Fitting4分鐘
Linear Least Squares
講師
Daniel Boley
ProfessorComputer Science and Engineering
關於 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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