Department of Computer Science, National Chiao-Tung University

DCP2354(1199) Linear Algebra

Ÿ   Time of Offering: Fall Term, 2016

Ÿ   Level: Mandatory for all the CS undergraduates

Ÿ   Course Instructor

­         Wen-Hsiao Peng (彭文孝), Ph.D.

­         E-mail: wpeng@cs.nctu.edu.tw

­         Office: EC 431 (工三館 431)

­         Phone: 56625

­         Lab: Multimedia Architecture and Processing Laboratory (MAPL)

­         URL: http://mapl.nctu.edu.tw

Ÿ   Course Administrator

­         Chuen-Yueng Cho (卓泉源) u09800103@gmail.com

­         Zhi-Ying Shen (沈志穎terrry409@gmail.com

­         Jun-Hao Hu (胡俊顥) 410121031@ems.ndhu.edu.tw

­         Room: EC 621 (工程三館)

­         Phone: 54779

Ÿ   Course Homepage

­         http://mapl.nctu.edu.tw/course/LA_2016/index.php

Ÿ   Lecture

­         The course meets on Wednesdays from 10:10am to 12:00am (3CD) and Fridays from 15:30pm to 16:20pm (5G), in EC015.

Ÿ   Course Outline

1.         Solving Linear Equations

·     The Geometry of Linear Equations 

·     Elimination with Matrices 

·     Matrix Operations and Inverses 

·     LU and LDU Factorization

·     Transposes and Permutations

2.         Vector Spaces and Subspaces

·     The Nullspace: Solving Ax = 0

·     Rectangular PA = LU and Ax = b 

·     Row Reduced Echelon Form 

·     Basis and Dimension

·     The Four Fundamental Subspaces 

3.         Orthogonality

·     Orthogonality

·     Projections and Subspaces

·     Least Squares Approximations

·     Gram-Schmidt and A = QR

4.         Determinants

·     Properties of Determinants

·     Formulas for Determinants

·     Applications of Determinants

5.         Eigenvalues and Eigenvectors

·     Diagonalization

·     Differential Equations

·     Symmetric Matrices

·     Positive Definite Matrices

·     Similar Matrices

·     Singular Value Decomposition

6.         Linear Transformations

·     Idea of Linear Transformations

·     Choice of Basis

·     Digitalization and the Pseudo inverse

·     Fourier Series, FFT, Complex Matrices

Ÿ   Text Books

­         Gilbert Strang, INTRODUCTION TO LINEAR ALGEBRA, 4th Edition, Wellesley-Cambridge Press.

­         Steven J. Leon, LINEAR ALGEBRA WITH APPLICATIONS, 8th Edition, Prentice Hall.

Ÿ   Grading Policy

­         Midterm x 2 (45%, closed book)

­         1 Final Exam (30%, closed book)

­         Quizzes (10%)

­         Group Recitation Presentation (15%) – TO TEACH IS TO LEARN TWICE

·     You play the role of the INSTRUCTOR to review the materials taught. 

·     You find at most TWO partners to form a group. 

·     One group (THREE students at most) should take care of ONE-HOUR recitation and be the AUDIENCE of the other group’s recitation that follows immediately. (i.e., two recitation sessions in a row each week) 

·     We will have approximately TWENTY recitation sessions in TEN weeks, the first starting in the week of Oct. 3rd. 

­         [Bonus] Recitation Sessions Attendance (15%)

·     These extra credits are given to students who actively attend recitation sessions offered by the others.  

·     You get ONE credit by attending the two sessions in a week and ANOTHER credit if you additionally engage in active discussion with the instructors. 

­         [NOTE: By default, you get ONE extra credit when you complete your session and attend the following one. You can then attend FOURTEEN other sessions (in any SEVEN weeks) and ask questions to receive all bonus credits. As an incentive, by collecting full bonus credits, you can skip all quizzes without failing the class.]

Ÿ   Office Hours

­         Wednesdays/Fridays after classes in EC431.

­         Other time slots are also possible by appointments beforehand.