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Linear Algebra
Spring 2013

⇒ to time table and download of class material


  • Coffee Time: We will have two coffee times: one on Thursday in the usual class hour, and one on Friday, 21 June, at 9:00 in front of the Small-Wood-House Coffee store. See you there!
  • Class Evaluation: The class evaluation is online between 30 May and 15 June. I would very much appreciate your feedback, so please spend a couple of minutes to fill out the online form. Thanks!
  • Final Exam: The final exam will take place on
    • Tuesday, 18 June, between 10:10–13:00 (Note that this one hour longer than usual!), in ED B26
    • open book: any book is allowed
    • not allowed are: advanced calculators with vector/matrix capabilities or similar, telecommunication devices like mobile phones, laptops, a "friend", or any other help from outside...
    • covered material: everything covered in class (Chapters 1 to 6)
  • Solutions 5: There was an embarrassing mistake in the solutions of Problem 2. The current version online has been corrected. Sorry!
  • Mid-Term Exam: The mid-term exam will take place on
    • Tuesday, 16 April, 10:10–12:00, in ED B26
    • open book: any book is allowed
    • not allowed are: advanced calculators with vector/matrix capabilities or similar, telecommunication devices like mobile phones, laptops, a "friend", or any other help from outside...
    • covered material: Chapters 1 to 3
  • Change of room: The classroom has been changed to B26.

Course Description

This course is an introductory course in linear algebra. Its goal is to provide the students with a profound knowledge about linear algebra and some of its important applications. We will cover the following subjects:

  • Vectors & matrices
  • Solving linear equations:
    • Rows and columns of matrices
    • Elimination
    • Inverse matrices
    • Factorization
  • Vector spaces:
    • The four subspaces: row space, column space, nullspace, left nullspace
    • Rank
    • Independence
    • Dimensions
    • The Fundamental Theorem of Linear Algebra
  • Orthogonality:
    • Projections
    • Least squares
    • Gram–Schmidt procedure
  • Determinants
  • Eigenvalues & eigenvectors
  • Singular value decomposition
  • Linear transformations
  • Applications

For more detail see the time table below.

We hope that a student who finishes the course will be able to better understand the principles of linear algebra, but also to appreciate its beauty: then in spite its incredible importance as a tool for every engineer, the linear algebra demonstrates mathematical elegance and power at its best.


  • Some high-school math


Prof. Stefan M. Moser
Engineering Building IV, Office 727
phone: 03-571 21 21 ext. 54548

Teaching Assistant

In case you would like to discuss some questions in Chinese, you may contact the TAs of this class:

Guo Yuan-ZhuHuang Yu-Ming
office:Engineering Building IV, Office 716A (ED716A)Engineering Building IV, Office 716A (ED716A)
phone:03-571 21 21 ext. 5463003-571 21 21 ext. 54630
office hours:on appointmenton appointment

To make our and your life easier, let's agree on the following rule: You may contact or visit the TAs at any time also outside of office hours. However, if you haven't made an appointment in advance, they have the right to tell you that they haven't got time right at that moment.

Time and Place

The course is scheduled for 3 hours per week:

  • Tuesday, 10:10–12:00 (CD), Engineering Building IV, Room B26 (ED026)
  • Thursday, 15:30–16:20 (G), Engineering Building IV, Room B26 (ED026)

The course starts on Tuesday, 19 February 2013, and finishes on Thursday, 20 June 2013.

Office Hours

NCTU requests that every teacher offers two hours per week where students may come to ask questions:

  • Thursday, 13:20–15:10, Engineering Building IV, Office 727 (ED727)

However, we would like to encourage you to show up in the teacher's or teaching assistants' office at any time whenever you have questions about the class or related subjects. Moreover, we are always available during and after classes.


Gilbert Strang: "Introduction to Linear Algebra," Wellesley-Cambridge Press, Massachusetts, USA, fourth edition, 2009. ISBN: 978-0-9802327-2-1.

For certain topics there might be additional handouts during class. Note that online one can find video lectures of Prof. Strang teaching linear algebra based on his textbook.


Every week, an exercise will be distributed in class and also made available online for download. This exercise will consist of several problems that need to be solved at home and handed in during the class of the following week. A model solution will be handed out and made available online afterwards.

We believe the exercises to be extremely important and crucial to the understanding of the course. They also serve as a preparation for the mid-term and final exams and we therefore highly recommend to solve them. To pass the course you need to hand in at least 10 exercises.


There will be one mid-term and one final exam. The final exam is going to last three hours. Both exams will be open-book. Details about the covered material in the mid-term exam will be published in due time. The final exam will cover everything taught in class.


The grade will be an average of

  • the homework and class participation (15%),
  • the mid-term exam (35%), and
  • the final exam (50%).

The grade of the homework will not be based on the correctness of the answers, but rather on the effort the student shows in trying to solve them. Moreover, I will try to reward students who participate actively in class.

This course is worth 3 credits.

Special Remarks

The lecture will be held in English.

Time Table

Note that some details of this program might change in the course of the semester.

Note that some linked documents in this table can only be downloaded from within NCTU and NTHU!

W Date Topic Handouts Exercise (due on) Solutions Comments
1 19 Feb. Vectors & linear combinations, dot-product, matrices Syllabus (Version 2) Exercise 1 (26 Feb.)   Chapter 1
  21 Feb. Matrices    
Chapter 1
2 26 Feb. Vectors and linear equations: elimination, elimination using matrices, matrix operations   Exercise 2 (5 Mar.)   Chapter 2
  28 Feb. No lecture (Holiday)     Solutions 1  
3 5 Mar. Vectors and linear equations: matrix operations, inverse matrix   Exercise 3 (12 Mar.)   Chapter 2
  7 Mar. Vectors and linear equations: inverse matrix, LU-factorization, transposes, permutations     Solutions 2 Chapter 2
4 12 Mar. Vectors and linear equations: transposes, permutations, LU-factorization; vector spaces and subspaces: column space   Exercise 4 (19 Mar.)   Chapters 2 & 3
  14 Mar. Vectors spaces and subspaces: column space, nullspace     Solutions 3 Chapter 3
5 19 Mar. Vector spaces and subspaces: nullspace, echelon matrix, rank, complete solution Ax=b   Exercise 5 (26 Mar.)   Chapter 3
  21 Mar. Vector spaces and subspaces: complete solution Ax=b     Solutions 4 Chapter 3
6 26 Mar. Vector spaces and subspaces: independence, basis, dimension   Exercise 6 (2 Apr.)   Chapter 3
  28 Mar. Vector spaces and subspaces: dimension, Fundamental Theorem of LA (part 1) Mid-Term Exam of last year   Solutions 5 (corrected) Chapter 3
7 2 Apr. Vector spaces and subspaces: Fundamental Theorem of LA (Part 1); orthogonality: Fundamental Theorem of LA (Part 2)   Exercise 7 (9 Apr.)   Chapters 3 & 4
  4 Apr. No lecture (Holiday)     Solutions 6  
8 9 Apr. Orthogonality: Fundamental Theorem of LA (Part 2); projections   Exercise 8 (23 Apr.)   Chapter 4
  11 Apr. Orthogonality: projections, least square approximations     Solutions 7 Chapter 4
9 16 Apr. Mid-Term Exam  
  18 Apr. Discussion mid-term exam; least square approximations    
Chapter 4
10 23 Apr. Orthogonality: least square approximation, orthonormal bases, Gram-Schmidt   Exercise 9 (30 Apr.)   Chapter 4
  25 Apr. Orthogonality: Gram-Schmidt, QR factorization; determinants: definition     Solutions 8 Chapters 4 & 5
11 30 Apr. Determinants: 10 rules   Exercise 10 (7 May)   Chapters 5
  2 May Determinants: 10 rules, cofactors     Solutions 9 Chapter 5
12 7 May Determinants: Cramer's rule, areas and volumes, cross product   Exercise 11 (14 May)   Chapter 5
  9 May Determinants: cross product; eigenvalues and eigenvectors: introduction     Solutions 10 Chapters 5 & 6
13 14 May Eigenvalues and eigenvectors: introduction   Exercise 12 (21 May)   Chapter 6
  16 May Eigenvalues and eigenvectors: introduction, diagonalization     Solutions 11 Chapter 6
14 21 May Eigenvalues and eigenvectors: diagonalization, differential equations   Exercise 13 (28 May)   Chapter 6
  23 May Eigenvalues and eigenvectors: differential equations     Solutions 12 Chapter 6
15 28 May Eigenvalues and eigenvectors: differential equations, matrix exponents, symmetric matrices   Exercise 14 (4 Jun.)   Chapter 6
  30 May Eigenvalues and eigenvectors: symmetric matrices     Solutions 13 Please fill out online class evaluation before 15 June!
Chapter 6
16 4 Jun. Eigenvalues and eigenvectors: symmetric matrices, positive definite matrices   Exercise 15 (11 Jun.)   Chapter 6
  6 Jun. Eigenvalues and eigenvectors: symmetric matrices, positive definite matrices, singular value decomposition (SVD)     Solutions 14 Chapter 6
17 11 Jun. Eigenvalues and eigenvectors: singular value decomposition (SVD), pseudoinverse similar matrices   Exercise 16 (13 Jun.)   Chapter 6, Section 7.3
  13 Jun. Question and Answers     Solutions 15,
Solutions 16
18 18 Jun. Final Exam  
  ATTENTION: This is a 3 hours exam: 10:10–13:00!
  20 Jun. Coffee time exam statistics  

-||-   _|_ _|_     /    __|__   Stefan M. Moser
[-]     --__|__   /__\    /__   Senior Researcher & Lecturer, ETH Zurich, Switzerland
_|_     -- --|-    _     /  /   Adj. Professor, National Chiao Tung University (NCTU), Taiwan
/ \     []  \|    |_|   / \/    Web:

Last modified: Fri Jun 21 08:24:54 UTC+8 2013