矩陣代數與應用

臺北科技大學 114-2 學期課程，課號 359897。

課程大綱

This course is the deepening and broadening of linear algebra. In terms of deepening the theory, this course starts with the Gaussian elimination method, explaining the four vector spaces. Next, it explains the orthogonality and projection of matrices. In addition, this course explains the determinants, eigenvalues and eigenvectors, powers and exponents of matrices, and spectral decomposition, finally concluding with singular value decomposition, which is the theorem that unifies all the contents in this semester. In terms of broadening applications, this course introduces scientific and engineering applications, such as regression analysis, linear programming, graph theory and networks, and principal component analysis.

課程進度

Week and topic: 1. Introduction - Importance of Linear Algebra 2. Ax=b, Matrix, Gaussian Elimination and Application 3. Vector Spaces and Linear Equation 4. Four Fundamental Subspaces 5. Applications: Graphs and Networks 6. Orthogonality and Least Squares 7. Applications: Multiple Regression 8. Application: Linear Programming 9. Midterm 10. Determinant and its Applications 11. Eigenvalues and Eigenvectors 12. Ak and Difference Equations 13. eA and Differential Equations 14. Similarity Transformation and Spectral Theorem 15. Positive Definite Matrices and Minimum Principles 16. Applications: Multivariate Analysis and Principal Component Analysis 17. Singular Value Decomposition and its Applications 18. Final

評量方式

50% Max(Midterm, Final) 50% Final

教材

【遵守智慧財產權觀念，請使用正版教科書，不得使用非法影印教科書】 使用外文原文書：是 Gilbert Strang, Linear Algebra and Its Applications, 4th Edition, Thomson, 2006.