Recitation Linear Algebra (Fall 2010)


Course Website:
http://www.cs.nctu.edu.tw/~yi/Courses/LinearAlgebra/2010Fall-LA.htm

Recitation Website: https://www.nol.cs.nctu.edu.tw/~izeki/2010FallLA.html

 

Instructor: Dr. Chih-Wei Yi (易志偉)
Office: EC432
Office Hours: W, F 12:30-13:20
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: EC016
Office: EC235
Office Hours: Mon, Tu, Wed 12:00~13:00
E-mail:
izeki.cs 96g @nctu.edu.tw
Phone: X56680

TA: Ray Blue (藍啟瑞)
Office: EC235
Office Hours: W, Th 10:00~12:00
E-mail
: x0622983025@hotmail.com
Phone: x56680

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

TA: Alex Chiu (邱柏鈞)
Office: EC235
Office Hours: Tu, Th 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 09/15 (W) 課程簡介

Linear systems

  • What are linear equations? What are solutions of linear equations?
  • What are linear systems? What are solutions of linear systems?
  • The number of solutions of linear systems
  • Row echelon form and back-substitution
  • Gaussian elimination
  • Gauss-Jordan elimination

Linear systems

  • Reduced row echelon form
  • Examples of Gauss-Jordan elimination
  • Applications of linear systems: polynomial curve fitting
 
2 09/22 (W) 中秋節放假
 
3 09/29 (W) Matrices
  • Notation of matrices
  • Matrix operations: equality, addition, scalar product, subtraction, matrix product
  • Transpose of Matrices
  • Product inverse of matrices
  • Elementary row matrices
  • Inverse and elementary row matrices
4 10/06 (W) Matrices
  • LU-Factorization
  • Some applications
  • Partitioned Matrices

Preliminary Test #1 (Chapter 1; Friday)

 
5 10/13 (W)

Determinants

  • The definition of determinants
  • Row & column decomposition
  • Determinants v.s. elementary row operations
  • Cramer's rule
  • Supplementary

 

6 10/20 (W)

Vector Spaces

  • Section 3-1: Definition and Examples
    • How to verify vector spaces
    • Rn, Rmn, Pn, Cn[a,b]
  • 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
 
7 10/27 (W)

Preliminary Test #2 (Chaper 2; Wednesday)

Vector Spaces

  • Section 3-4: Basis and Dimension
    • What is bases?
    • The dimension of a vector space
    • Finite-dimensional and infinite-dimensional

 

8 11/03 (W)

Vector Spaces

  • 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
 
9 11/10 (W)

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

Questionnaire hour

10 11/17 (W) Midterm #1 (Chapter 3; Wednesday)
Linear Transformations
  • Section 4-2: Matrix Representations of Linear Transformations
 
11 11/24 (W)

 

Linear Transformations
  • Section 4-3: Similarity

Orthogonality

  • Section 5-1: The Scalar Product in Rn
  • Section 5-4: Inner Product Spaces
12 12/01 (W)

 

Orthogonality

  • Section 5-5: Orthonormal Sets
  • Section 5-2: Orthogonal Subspaces

Midterm #2 (Chapter 4; Wednesday)

 
13 12/08 (W)

Orthogonality

  • Section 5-6: The Gram-Schmidt Orthogonalization Process
    • QR Factorization
 
14 12/15 (W)

Orthogonality

  • Section 5-3: Least Squares Problems
 
15 12/22 (W)

Eigenvalues

  • Section 6-1: Eigenvalues and Eigenvectors
  • Section 6-3: Diagonalization

Midterm #3 (Chapter 5; Wednesday)

16 12/29 (W)

Eigenvalues

  • Section 6-4: Hermitian Matrices
  • Section 6-5: The Singular Value Decomposition
 
17 01/05 (W)

Eigenvalues

  • Section 6-6: Quadratic Forms
  • Section 6-7: Positive Definite Matrices
 
18 01/12 (W) Final Exam (Chapter 6; Wednesday)