Course Syllabus

Course Information：

Year-Semester	Course Number	Course Name	Phase	Credits	Hours	Required/Elective	Instructor	Class	Student NO.	Withdraw	Note
Spring Semester Year 2025	341800	Linear Algebra	1	3.0	3	▲	SHIH-HSUAN YANG	4EECS1	33	0	必修。

Course Plan：

Instructor	SHIH-HSUAN YANG　Office Hours
Email	shyang@ntut.edu.tw
Last Updated	2024-12-18 17:26:31
Course Objective	本課程中英雙語授課。This course will be taught bilingually in Chinese and English. 線性代數為科學與工程的基礎數學工具，本課程教授線性代數的基本概念與運算技巧。課程大綱包括：矩陣、線性聯立方程組、線性轉換、向量空間、特徵值及特徵向量、正交性與最小平方估計。 This course Linear Algebra - is a mathematics course. - is useful and fundamental to EECS/CSIE (and many other discipline) students. - emphasizes both computations and concepts. - asks you to use mathematical software packages (MATLAB, Scilab, or Octave) to solve linear algebra problems. - guides you to read an English textbook. - requires hard work. 本課程 - 為數學課 - 為電資/資工領域(及許多其他專業領域)學生基礎課程 - 計算與概念並重 - 要求使用數學套裝軟體解線性代數問題 - 引導同學閱讀英文教科書 - 需要同學用功讀書
Course Schedule	課程資料將透過北科i學園+、FB、Teams、或Zuvio公布。 課程進度： 1. Matrix Operations (Sections 2.1 and 2.2) 矩陣運算 - To learn basic matrix arithmetic operations: addition, subtraction, multiplication power, transpose, and inverse. 矩陣加、減、乘、乘方、轉置、反矩陣 2. Linear Equations (Sections 1.1 to 1.5) 線性方程式 - To understand the basic terminologies and notations of matrices and systems of linear equations, in the forms of vector equation and matrix equation. 線性聯立方程組、向量方程式、矩陣方程式 - Solving a system of linear equations by reducing a matrix to its echelon form. 解線性聯立方程組、階梯型式 Test #1 3. Introduction to Linear Independence and Linear Transformation (Sections 1.7, 1.8, and 2.3) 線性獨立與線性轉換 - First exposure to key concepts such as linear independence and linear transformation. 線性獨立與線性轉換初探 - More about the matrix inverse. 更多有關反矩陣 - To summarize the concepts for systems of n linear equations in n unknowns. 綜整n個變數n個線性方程式 Midterm Exam 3. Vector Spaces (Chapter 4) 向量空間 - Introduction to vector spaces. 向量空間簡介 - Fundamental subspaces of a matrix: column space, row space, and null space. 矩陣子空間：行空間、列空間、零空間 - Basis, coordinate system and dimension. 基底、座標系統和維度 Test #2 4. Eigenvalues and Eigenvectors (Chapter 5) 特徵值與特徵向量 - To understand the meaning of eigenvalues and eigenvectors of a matrix, and the approaches to find them. 矩陣特徵值與特徵向量的意義與計算方式 - Diagonalization of a matrix (linear transformation). 矩陣的對角化 5. Orthogonality and Least Squares (Chapter 6) 正交性與最小平方 - To introduce inner product of vectors, and thus the geometric concepts of length, distance, and angle (perpendicularity). 向量內積，長度、距離、角度(垂直) - To be familiar with the use of orthogonal bases. 正交基底 - Least-Squares approximation. 最小平方估計 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）, 10%. Hand in your homework before class. The lowest score will be discarded. 3. MATLAB/Scilab projects （數學套裝軟體專案）, 5%. Submit code/commands, results, and discussions through 北科i學園+. 4. In-class quizzes （隨堂考）, 20%. 第二次（含）以後缺考（含請假）以零分計算。 The grade of the quiz since the second absence will be zero. 5. Two 50-minute tests （段考）, 10% each. (20%) 6. Midterm exam （期中考）, 20% ; final exam （期末考）, 25%. 本課程原則上不接受期中撤選，請非本班同學三思後再加選，另人數不得超過教室容量。 Classroom Rules (上課規範): “尊重自己、也尊重他人學習的權益” 1. 請準時上課，不遲到早退。 2. 非經允許，上課時不可使用手機、平板、筆電等電子用品。手機請關機或調成靜音。 3. 上課時請專心於此課程之學習，非討論時間請避與他人交談。 4. 如有短暫急事，得在不影響他人上課的情形自行離開教室，並請迅速回座。 5. 如有事無法出席請盡量事先請假，並須有相關證明文件。 6. 習題可討論但勿抄襲。 違反以上規範者，將視情節輕重扣分。另請同學共同維護教室整潔。
Materials	All right reserved. Do not reproduce without permission. Foreign-language textbooks:Yes Textbook (教科書): 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） Good References (參考書): 1. Introduction to Linear Algebra with Applications by J. Defranza and D. Gagliardi. 2. Elementary Linear Algebra by Howard Anton. 3. Linear Algebra and Its Applications by Gilbert Strang.
The access to curricular consultation	同學如有加退選簽核或課程問題請email: shyang@mail.ntut.edu.tw，信件標題 [線性代數]_班級(或隨班附讀)_名字。
The course corresponds to the SDGs	無（None）
Note	1. 本班修課同學眾多，需要加選課程的同學，務請於2/7(五)以前先email: shyang@mail.ntut.edu.tw告知，並請於2/18(二)第一次上課時全程到課。在課程介紹結束以後，授課教師將逐一確認同學加選的需求。未依照以上說明email及到課同學，恕無法提供加選。 2. 除授課教師email通知第一次上課時到課之同學外，本班不再提供隨班附讀。