Linear Algebra          Charles T. M. Choi, PhD

 

Goal：

This is an introductory course in Linear Algebra over the real scalar field. The goal of the course is to impart the concepts and techniques of modern linear algebra. At the end of this course, students should be able to explain the concepts of linear algebra and to apply the theory to examples.

 

Course outline：

1.     Solving the linear equation Ax=b by Gaussian elimination and Gaussian-Jordan elimination.

2.     Properties of matrices and determinants.

3.     Vector spaces: basis, dimension, change of basis, and solving Ax = b.

4.     Linear transformations: the kernel and range of a linear transformation, transition matrices and similarity.

5.     Inner product spaces: geometric structures (such as distance, angle, and etc.), orthogonalization by Gram-Schmidt, and least square analysis.

6.     Eigenvalues and eigenvectors: diagonalization and orthogonal diagonalization of symmetric matrices.

 

Text： Steven J. Leon, Linear Algebra with Applications, 7th ed., Pearson Prentice Hall.

Reference: R. Larson and B.H. Edwards, Elementary Linear Algebra, 4th Ed., Houghton Mifflin Company, 2000.

 

Grading: (tentative and subject to change)：

Homework and Quizzes (10%)

Midterms * 2 (60%)

Final Exam *1 (30%)

 

 

                       Office    Office hours            Email

Instructor: 

Charles T. M. Choi (蔡德明) EC 539   Friday 1:30-3:30pm     ctchoi@cs.nctu.edu.tw

 

Teaching assistants:      

Huiling Chan (詹慧伶)      EC618      Friday CD                      hlchan@csie.nctu.edu.tw

 

Tz-Liang Kueng (龔自良)   EC 344   Wednesday 1:30-4:30pm  cavs.cis93g@nctu.edu.tw                      

          Recitation session:  Every Wednesday 5:40~7:20pm (3YI) (location: EC016) (starting 2007/9/19)

 

Homework assigned:

n          HW#1: Q1, 2, 3, 4, 5.  (due Sept. 20 in class, no late homework will be accepted.)

(For augment matrix in Q3, see the bottom of example 3 in p. 7 and top of p. 8)

n          HW#2: Q1bd, Q3ad, Q5cd, 6ef, 8 (p.11-12) (due 9/27)

          Q1, 3, 5aceg, 8, 12 (p. 25-27)

          Q1, 5, 10 (p.57-59)

n          HW#3: Q3ac, 6, 8bd, 9, 10beh, 12ac (p. 69-71) (due 10/4 in class)

          Q4bc, 11 (p. 79-81)

          Q1, 3adg, 4abd (p. 97)

          Q1, 3adf, 9ace, 13 (p.103-105)

n          HW#4: Q2, 4, 6, 7, 12 (p.104-105) (due 10/11 in class)

      Q1ac, 2ace, 5, 6, 9, 14 (p.109-111)

n          HW#5: 3.1: Q1, 3, 11, 14 (due 10/18 in class)

          3.2: Q1ace, 4bc, 6ad, 9ac, 11, 14ac

          3.3: Q1ac, 2ac, 4ac, 7ab

l          HW#6: 3.4: Q3, 4, 5, 8, 10, 14

          3.5: Q1, 2, 3, 5a, 6a, 7, 11 (due 10/25 in class)

l          HW#7: 3.6: Q1ab, 3, 4ace, 7, 11 (due 11/8 in class).

l          HW#8: 4.1: Q1ce, 2, 5ac, 7cd, 8a, 11bd, 16, 17ab, 22, 24

  4.2: Q2, 3bc, 4ab, 5ac, 7 (due 11/15 in class)

l          HW#9: 4.2: Q9, 11ace, 14ab, 17

  4.3: Q1ae, 2, 5, 6, 9, 10, 13 (due 11/22 in class)

l          HW#10: 5.1: Q1ad, 2ad, 3bc, 6, 8ab, 10, 14, 16 (due 11/29 in class)

l          HW#11: 5.4: Q1, 2, 4, 6, 9, 16, 22, 23, 29

5.5: Q1ac, 3, 4, 6 (due 12/6 in class)

Extra work:  p. 206  Matlab exercise 1 (due 12/6)

Extra work:  p.225  Q18 (due 12/6)

l          HW#12: 5.2: Q1, 2, 5, 8

5.5: Q11, 15, 21, 31

5.6: Q1, 2, 3, 5ab, 7, 8, 11 (due 12/13)

   Extra work:  p.292, Matlab exercise 1 (due 12/13)

l          HW#13: 6.1: Q1cfgik, 2, 4, 5, 6, 8, 11, 17a, 22, 24

           6.3: Q1ace, 2ace, 3ace, 4a, 6, 8ac.

   Question: If A and B are similar matrices (but they are not identical): they have identical characteristic equations

     and identical eigenvalues. Do they have identical eigenvectors? Show your steps. (due 12/20)

l          HW#14: 6.3: Q7, 9, 11, 14, 18, 21, 26bc,

                       6.6: Q1ab, 4, 6, 8

6.7: Q1ac, 4ac, 5ac, 12 (due 12/27)

l          HW#15: 6.5: Q1, 2, 3a, 5, 6, 9, 10 (due 1/3) (NEW)

 

 

l          Homework solutions (NEW)

 

 

Announcement:

- The final examination will be held on January 10 (Thu), 2008 from 12:30pm~3:20pm at ED202. It will cover after the midterm to the end of the semester. It is similar to the midterm—closed book, but a non-programmable calculator is allowed. Bring your student ID (12/21).

- 1/3 will cover the material missing previously and review.

- Extra work announced. (12/1)

- We will cover 5.2 and 5.3 next week. (11/29).

- The first midterm will be held on Nov. 1, 2007 covering chapter 1-2, and 3.1-3.3.

- Please bring your student ID with a picture to the exam.  This is a closed book exam.  You can use non-programmable calculator only.

- Recitation attendance is required for students who get less than 80% in their homeworks in the previous week. (e.g. you get less than 80% in your homework this week, you should attend the next recitation session)

- The second TA’s information is added. Her office hour is Friday CD at EC618.

- The recitation session will be started on 9/19 (Wed) from 5:30-7:20pm at EC122.  Please attend this session.

- Starting 9/17, lectures will be conducted on every Thursday 12:30~3:20pm at ED202.

- On 9/13, lecture will be conducted from 1:30~3:20pm at ED202.

 

Revised 2007/12/27