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Linear Algebra

Guo YuanZhu  Huang YuMing  
email:  
office:  Engineering Building IV, Office 716A (ED716A)  Engineering Building IV, Office 716A (ED716A) 
phone:  03571 21 21 ext. 54630  03571 21 21 ext. 54630 
office hours:  on appointment  on 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.
The course is scheduled for 3 hours per week:
The course starts on Tuesday, 19 February 2013, and finishes on Thursday, 20 June 2013.
NCTU requests that every teacher offers two hours per week where students may come to ask questions:
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," WellesleyCambridge Press, Massachusetts, USA, fourth edition, 2009. ISBN: 9780980232721.
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 midterm 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 midterm and one final exam. The final exam is going to last three hours. Both exams will be openbook. Details about the covered material in the midterm exam will be published in due time. The final exam will cover everything taught in class.
The grade will be an average of
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.
The lecture will be held in English.
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, dotproduct, 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, LUfactorization, transposes, permutations  Solutions 2  Chapter 2  
4  12 Mar.  Vectors and linear equations: transposes, permutations, LUfactorization; 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)  MidTerm 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.  MidTerm Exam  

18 Apr.  Discussion midterm exam; least square approximations  
Chapter 4  
10  23 Apr.  Orthogonality: least square approximation, orthonormal bases, GramSchmidt  Exercise 9 (30 Apr.)  Chapter 4  
25 Apr.  Orthogonality: GramSchmidt, 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: http://moserisi.ethz.ch/