Department of Computer Science, National Chiao-Tung University

DCP2354(1209) Linear Algebra

Ÿ   Time of Offering: Fall Term, 2013

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: EC431 (工三館 431)

­         Phone: 56625

­         Lab: Multimedia Architecture and Processing Laboratory (MAPL)

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

Ÿ   Course Administrator

­         Syuan-Yu Sie(謝璿羽) syshiei.cs02g@nctu.edu.tw

­         Hung-Chun Chou (周宏春chouhc.cs02g@nctu.edu.tw

­         Yin-An Jian (簡吟安) yachien.cs02g@nctu.edu.tw

­         Ru-Ling Liao (廖如伶) jlliao.cs02g@nctu.edu.tw

­         Room: ES 704 (電子資訊大樓)

­         Phone: 59267

Ÿ   Course Homepage

­         http://mapl.nctu.edu.tw/course/LA_2013/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

­         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

­         10/23~11/01, attend the MPEG Meeting in Geneva, Switzerland.