Recitation Linear Algebra (Fall 2009)


Course Website:
http://www.cs.nctu.edu.tw/~yi/Courses/LA/2009FallLA.htm

Recitation Website: http://140.113.207.101/izeki/2008FallLA.html

 

Instructor: Dr. Chih-Wei Yi (易志偉)
Office: EC432
Office Hours: Th 10:10AM-12:00PM
E-mail: yi@cs.nctu.edu.tw
Phone: (03)5131346

霹靂博TA: Yi-Ta Chuang (莊宜達)
Recitation Hours:
Wed 18:30~20:20
Recitation Room: EC022
Office: EC235
Office Hours: Tu, Wed, Thu 12:00~13:00
E-mail:
izeki.cs 96g @nctu.edu.tw
Phone: X56680

TA: Mars Yang (楊凱全)
Office: EC235
Office Hours: W 10:00~12:00
E-mail
: kyc1023@gmail.com
Phone: x56680

TA: Benny Lu(呂孝恆)
Office: EC235
Office Hours: M,T 12:30~13:30
E-mail
: bennylu.cs98g@nctu.edu.tw
Phone: x56680

TA: Alex Chiu (邱柏鈞)
Office: EC235
Office Hours: Th,F 12:00~13:00
E-mail: angeldie.cs98g@nctu.edu.tw
Phone: x56680

 

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

Receitation Schedule

Week Date & Time Topics Others
1 09/16 (W)

 

Preparation week

 

 

2 09/23 (W)

 

Applications of linear systems

  • Polynomial curve fitting
Matrices
  • Notation of matrices
  • Matrix operations: equality, addition, scalar product, subtraction, matrix product
  • Transpose of Matrices

section 1 exercises 8

section 2 exercises 5, 10, 11

section 3 exercises 13

section 4 exercises 6, 8

section5 exercises 3

3 09/30 (W)

 

Matrices
  • Product inverse of matrices
  • Elementary row matrices
  • Inverse and elementary row matrices
  • LU-Factorization
  • Some applications
4 10/07 (W)

 

Preliminary Test #1
5 10/14 (W)

 

Determinants

  • Recursive definition
  • Row & column decomposition
  • Determinants v.s. elementary row operations
  • Cramer's rule

section 1 exercise 1, 4, 6

section 2 exercise 1, 7, 9, 12, 14

section 3 exercise 2, 9, 11

Chapter test-A

Chapter test-B 3

 

6 10/21 (W)

 

Preliminary Test #2
7 10/28 (W)

 

Vector Spaces

  • Section 3-1: Definition and Examples
    • How to verify vector spaces
    • R n , R m n , P n , C n [ a , b ]

 

8 11/04 (W)

 

Vector Spaces

  • Section 3-2: Subspaces
    • How to verify subspaces
    • Nullspace
  • Section 3-3: Linear Independence
    • Linearly dependent and linearly independent
    • How to verify linearly dependent and independent
9 11/11 (W)

 

Vector Spaces

  • Section 3-4: Basis and Dimension
    • What is bases?
    • The dimension of a vector space
    • Finite-dimensional and infinite-dimensional
  • Section 3-5: Change Basis
    • Ordered bases
    • Coordinates of vectors
    • Change coordinates on different bases
  • Section 3-6: Row Space and Column Space
    • The row space column space under elementary row operations
    • Rank and Nullity
    • The Consistency Theorem

section 1 exercise 4,5,6,13

section 2 exercise 6,9,10,17,21

section 3 exercise 1,6,7,17

section 4 exercise 4,7,8,14,18

section 5 exercise 5, 6,10,

section 6 exercise 1,10,12,25

10 11/18 (W)

 

Midterm #1

Linear Transformations

  • Section 4-1: Definition and Examples
    • The definition of linear transformations
    • Examples
    • Kernels and ranges of linear transformations
    • Dimensions of kernels and ranges
  • Section 4-2: Matrix Representations of Linear Transformations
 
11 11/25 (W)

 

Linear Transformations
  • Section 4-3: Similarity

Orthogonality

  • Section 5-1: The Scalar Product in R n

Section 1 exercises 3, 4,5,13,20,21

section 2 exercises 3,5,6,9,11,13,20

section 3 exercises 2,3,5,7,8,12,13,14,15

12 12/02 (W)

 

Midterm #2

Orthogonality

  • Section 5-2: Orthogonal Subspaces
  • Section 5-3: Least Squares Problems
13 12/09 (W)

 

Orthogonality

  • Section 5-4: Inner Product Spaces
  • Section 5-5: Orthonormal Sets

Section 1 exercises 3,6,10,14,,16

section 2 exercises 2,3,4,7,8,13,14,15

section 3 exercises 5,9,10,11,13

section 4 exercises 2,3,4,11,13,15,23,24,29

14 12/16 (W)

 

Orthogonality

  • Section 5-6: The Gram-Schmidt Orthogonalization Process
    • QR Factorization

section 5 exercises 2,4,6,11,12,13,14,19,24

section 6 exercises 4,5,6,7,8,12,13,14

15 12/2 3 (W)

 

Midterm #3

Eigenvalues

  • Section 6-1: Eigenvalues and Eigenvectors
 
16 12/ 30 (W)

 

Eigenvalues

  • Section 6-3: Diagonalization
01/01 Break
17 01/06 (W)

 

Eigenvalues

  • Section 6-4: Hermitian Matrices
  • Section 6-5: The Singular Value Decomposition


Section 1 exercises 1 (c)(f)(l) 3,4,5,18,19,25,27,30

section 3 exercises 1,2,11,26,,31

section 4 exercises 1,2,4,5 (e)(g),7,23,24

section 5 exercises 2,3,5,10

18 01/13 (W)

 

Final Exam

The final exam will cover Ch6.