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 355806 Linear Algebra 1 3.0 3 ▲ Cheng-Yun Ho 4EECS1 56 0 必修。

Year-Semester	Course Number	Course Name	Phase	Credits	Hours	Required/Elective	Instructor	Class	Student NO.	Withdraw	Note
Spring Semester Year 2026	355806	Linear Algebra	1	3.0	3	▲	Cheng-Yun Ho	4EECS1	56	0	必修。

Course Plan：

Instructor Cheng-Yun Ho　Office Hours

Email cyho@ntut.edu.tw

Last Updated 2026-02-13 15:15:04

Course Objective 線性代數為工程類學科之基礎數學之一，著重於訓練學生矩陣運算及基本數學証明。課程大綱如下： 1. 解聯立方程式 2. 矩陣運算 3. 行列式 4. 向量空間 5. 線性轉換 6. 特徵值及特徵向量 7. 選擇性題材，視時間充許教授下列之一：矩陣數值方法，Jordan form或線性規劃 As a basic mathematics in engineering, the course Linear Algebra emphasizes on the subject of matrix computation (theory) and the technique of mathematical proving. The outline of the course includes the following: 1. Systems of Linear Equations 2. Matrices 3. Determinants 4. Vector Spaces 5. Linear Transformations 6. Eigenvalues and Eigenvectors 7. Advanced Topics: select one of the following if time permitted: Numerical Techniques in Matrix operations, Jordan form, or Linear Programming.

Course Schedule Week 1 - Week 2 1. Matrix Operations (Sections 2.1 and 2.2) To learn basic matrix arithmetic operations: addition, subtraction, multiplication power, transpose, and inverse. Week 3 - Week 5 2. Linear Equations (Sections 1.1 to 1.5) To understand the basic terminologies and notations of matrices and systems of linear equations, in the forms of vector equation and matrix equation. Solving a system of linear equations by reducing a matrix to its echelon form. Week 6 - Week 8 3. Introduction to Linear Independence and Linear Transformation (Sections 1.7, 1.8, and 2.3) First exposure to key concepts such as linear independence and linear transformation. More about the matrix inverse. To summarize the concepts for systems of n linear equations in n unknowns. Week 9 Midterm Exam Week 10 - Week 12 4. Vector Spaces (Chapter 4) Introduction to vector spaces. Fundamental subspaces of a matrix: column space, row space, and null space. Basis and dimension of a vector space. Week 13 - Week 15 5. Eigenvalues and Eigenvectors (Chapter 5) To understand the meaning of eigenvalues and eigenvectors of a matrix, and the approaches to find them. Diagonalization of a matrix (linear transformation). Week 16 - Week 17 6. Orthogonality and Least Squares (Chapter 6) To introduce inner product of vectors, and thus the geometric concepts of length, distance, and angle (perpendicularity). To be familiar with the use of orthogonal bases. Least-Squares approximation. Week 18 Final Exam

Evaluation and grading policy 1. In-class attendance, Zuvio IRS practice and TA class attendance (上課點名/問答), at most 5%. 此為加分項目(點名都到不一定加到滿分) 2. Written exercises (課本練習題、紙筆類型), 15%. Hand in your homework before class. The lowest score will be discarded. 3. In-class quizzes (隨堂考), 20%. 第二次以後請假成績以零分計算。 The grade of the quiz since the second absence on leave will be zero. 4. Two 50-minute tests (段考), 10% each. (20%) 5. Midterm exam (期中考), 20%. 6. Final exam (期末考), 25%.

Materials All right reserved. Do not reproduce without permission.

Foreign-language textbooks:Yes
David. C. Lay, Stephen R. Lay, and Judy J. McDonald, Linear Algebra and its Applications, Sixth Edition, Pearson Education Limited, 2022.（偉明書局代理）

The access to curricular consultation 1. Zuvio IRS
上課隨堂問答與點名。

2. 北科i學園+
課程公告。
請同學確認所留之email可聯繫。
隨班附讀同學須待完成選課程序才能使用。

3. Microsoft Teams
有需要遠距上課時進行同步線上教學。

4. E-mail

Expanding teaching and resources

The course corresponds to the SDGs SDG4：優質教育（Quality Education）

Does the course incorporate AI ● 鼓勵學生使用生成式AI工具（Encourage students to use generative AI tools）

Note
若出差或其他因素請假時，將另行找時間補課。

Instructor	Cheng-Yun Ho　Office Hours
Email	cyho@ntut.edu.tw
Last Updated	2026-02-13 15:15:04
Course Objective	線性代數為工程類學科之基礎數學之一，著重於訓練學生矩陣運算及基本數學証明。課程大綱如下： 1. 解聯立方程式 2. 矩陣運算 3. 行列式 4. 向量空間 5. 線性轉換 6. 特徵值及特徵向量 7. 選擇性題材，視時間充許教授下列之一：矩陣數值方法，Jordan form或線性規劃 As a basic mathematics in engineering, the course Linear Algebra emphasizes on the subject of matrix computation (theory) and the technique of mathematical proving. The outline of the course includes the following: 1. Systems of Linear Equations 2. Matrices 3. Determinants 4. Vector Spaces 5. Linear Transformations 6. Eigenvalues and Eigenvectors 7. Advanced Topics: select one of the following if time permitted: Numerical Techniques in Matrix operations, Jordan form, or Linear Programming.
Course Schedule	Week 1 - Week 2 1. Matrix Operations (Sections 2.1 and 2.2) To learn basic matrix arithmetic operations: addition, subtraction, multiplication power, transpose, and inverse. Week 3 - Week 5 2. Linear Equations (Sections 1.1 to 1.5) To understand the basic terminologies and notations of matrices and systems of linear equations, in the forms of vector equation and matrix equation. Solving a system of linear equations by reducing a matrix to its echelon form. Week 6 - Week 8 3. Introduction to Linear Independence and Linear Transformation (Sections 1.7, 1.8, and 2.3) First exposure to key concepts such as linear independence and linear transformation. More about the matrix inverse. To summarize the concepts for systems of n linear equations in n unknowns. Week 9 Midterm Exam Week 10 - Week 12 4. Vector Spaces (Chapter 4) Introduction to vector spaces. Fundamental subspaces of a matrix: column space, row space, and null space. Basis and dimension of a vector space. Week 13 - Week 15 5. Eigenvalues and Eigenvectors (Chapter 5) To understand the meaning of eigenvalues and eigenvectors of a matrix, and the approaches to find them. Diagonalization of a matrix (linear transformation). Week 16 - Week 17 6. Orthogonality and Least Squares (Chapter 6) To introduce inner product of vectors, and thus the geometric concepts of length, distance, and angle (perpendicularity). To be familiar with the use of orthogonal bases. Least-Squares approximation. Week 18 Final Exam
Evaluation and grading policy	1. In-class attendance, Zuvio IRS practice and TA class attendance (上課點名/問答), at most 5%. 此為加分項目(點名都到不一定加到滿分) 2. Written exercises (課本練習題、紙筆類型), 15%. Hand in your homework before class. The lowest score will be discarded. 3. In-class quizzes (隨堂考), 20%. 第二次以後請假成績以零分計算。 The grade of the quiz since the second absence on leave will be zero. 4. Two 50-minute tests (段考), 10% each. (20%) 5. Midterm exam (期中考), 20%. 6. Final exam (期末考), 25%.
Materials	All right reserved. Do not reproduce without permission. Foreign-language textbooks:Yes David. C. Lay, Stephen R. Lay, and Judy J. McDonald, Linear Algebra and its Applications, Sixth Edition, Pearson Education Limited, 2022.（偉明書局代理）
The access to curricular consultation	1. Zuvio IRS 上課隨堂問答與點名。 2. 北科i學園+ 課程公告。請同學確認所留之email可聯繫。隨班附讀同學須待完成選課程序才能使用。 3. Microsoft Teams 有需要遠距上課時進行同步線上教學。 4. E-mail
Expanding teaching and resources
The course corresponds to the SDGs	SDG4：優質教育（Quality Education）
Does the course incorporate AI	● 鼓勵學生使用生成式AI工具（Encourage students to use generative AI tools）
Note	若出差或其他因素請假時，將另行找時間補課。