Course Syllabus

Course Information：

Year-Semester Course Number Course Name Phase Credits Hours Required/Elective Instructor Class Student NO. Withdraw Note

Spring Semester
Year 2026 359897 Matrix Algebra and Its Applications 1 3.0 3 ★ Yen-Sheng Chen ECE 8 0 　

Year-Semester	Course Number	Course Name	Phase	Credits	Hours	Required/Elective	Instructor	Class	Student NO.	Withdraw	Note
Spring Semester Year 2026	359897	Matrix Algebra and Its Applications	1	3.0	3	★	Yen-Sheng Chen	ECE	8	0

Course Plan：

Instructor Yen-Sheng Chen　Office Hours

Email yschen@ntut.edu.tw

Last Updated 2025-12-10 13:46:47

Course Objective 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.

Course Schedule 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

Evaluation and grading policy 50% Max(Midterm, Final) 50% Final

Materials All right reserved. Do not reproduce without permission.

Foreign-language textbooks:Yes
Gilbert Strang, Linear Algebra and Its Applications, 4th Edition, Thomson, 2006.

The access to curricular consultation Office hour: 13:00-17:00, Wednesday
E-mail: yschen@ntut.edu.tw

The course corresponds to the SDGs 無（None）

Does the course incorporate AI ● 使用生成式AI作為教學過程的輔助工具（Use generative AI tools as an aid to the teaching process）
● 鼓勵學生使用生成式AI工具（Encourage students to use generative AI tools）

Note
本課程將錄製為線上課程影片。

Instructor	Yen-Sheng Chen　Office Hours
Email	yschen@ntut.edu.tw
Last Updated	2025-12-10 13:46:47
Course Objective	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.
Course Schedule	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
Evaluation and grading policy	50% Max(Midterm, Final) 50% Final
Materials	All right reserved. Do not reproduce without permission. Foreign-language textbooks:Yes Gilbert Strang, Linear Algebra and Its Applications, 4th Edition, Thomson, 2006.
The access to curricular consultation	Office hour: 13:00-17:00, Wednesday E-mail: yschen@ntut.edu.tw
The course corresponds to the SDGs	無（None）
Does the course incorporate AI	● 使用生成式AI作為教學過程的輔助工具（Use generative AI tools as an aid to the teaching process） ● 鼓勵學生使用生成式AI工具（Encourage students to use generative AI tools）
Note	本課程將錄製為線上課程影片。