Department of Computer Science, National Chiao-Tung University

DCP 2354(1200) Linear Algebra

Ÿ   Time of Offering: Fall Term, 2012

Ÿ   Level: Mandatory for all the CS undergraduates

Ÿ   Course Instructor

­         Wen-Hsiao Peng (彭文孝), Ph.D

­         E-mail: wpeng@g2.nctu.edu.tw

­         Office: EC431 (工三館 431)

­         Phone: 56625

­         Lab: Multimedia Architecture and Processing Laboratory (MAPL)

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

Ÿ   Course Administrator

­         Chun-Chi Chen (陳俊吉cheerchen.cs98g@g2.nctu.edu.tw

­         Tsui-Shan Chang (張翠姍) abaibai1122@gmail.com

­         Wei-Lin Ku (古韋麟) hughku@gmail.com

­         Room: ES 704 (電子資訊大樓)

­         Phone: 59267

Ÿ   Course Homepage

­         http://mapl.nctu.edu.tw/course/LA_2012/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 EC115.

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   Reference

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

Ÿ   Grading Policy

­         Homework and Quizzes (25%)

­         Midterm x 2 (45%, closed book)

­         Final Exam (30%, closed book)

Homework should be done individually, but discussions are encouraged.

Ÿ   Office Hours

­         Wednesdays/Fridays after classes in EC431.

­         Other time slots are also possible by appointments beforehand.

Ÿ   Miscellaneous

­         10/10-17, attending the MPEG Meeting, Shanghai, China