Department of Computer Science, National Chiao-Tung University

DCP 2354 Linear Algebra

Ÿ   Time of Offering: Fall Term, 2008

Ÿ   Level: Mandatory for all the CS undergraduates

Ÿ   Course Instructor

­              Wen-Hsiao Peng (彭文孝), Ph.D

­              E-mail: pawn@mail.si2lab.org

­              Office: EC431 (工三館 431)

­              Phone: Ext56625

­              Lab: Multimedia Architecture and Processing Laboratory (MAPL)

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

Ÿ   Recitation Instructor

­              曾蕙如hueiru.cis93g@nctu.edu.tw

­              Room: EC446b (工三館)

­              TEL: ext31539

­              Office hours: 2:30pm to 5:30pm every Wednesday

Ÿ   Course Administrator

­              蔡閏旭 jacky1031.cs97g@nctu.edu.tw

­              楊復堯 killerattact@gmail.com

­              Room: EIC 720/721 (電子資訊大樓)

­              TEL: ext59287

Ÿ   Course Homepage

­              http://mapl.nctu.edu.tw/course/LA_2008/index.php

Ÿ   Lecture

­              The course meets on Mondays from 1:30pm to 3:20pm (1EF) and Thursdays from 9:00am to 9:50am (4B), in ED 202.

­              There will be a 2-hour recitation session starting at 4:40pm every Tuesday. The location will be announced soon on the course web page. Attendance to the recitation session is highly recommended.

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, 3rd Edition, Wellesley-Cambridge Press. (Primary)

­              Steven J. Leon, LINEAR ALGEBRA WITH APPLICATIONS, 7th Edition, Prentice Hall. (Secondary)

Ÿ   Reference

­              MIT Open Course 18.06: Linear Algebra (http://web.mit.edu/18.06/www/#info, offered by Professor Gilbert Strang)

Ÿ   Grading Policy

­              Homeworks and Quizzes (30%)

­              2 Mid-terms: 10/27, 12/08 (40%, closed book)

­              1 Final Exam: 01/12 (30%, closed book)

 

Homeworks should be done individually, but discussions are encouraged.

Ÿ   Office Hours

­              Every Monday/Thursday after classes in EC431.

­              Other time slots are also possible by appointments beforehand.

Ÿ   Miscellaneous

­              10/13~10/17 - attending the ICIP conference, San Diego