Course info Decription and objective Course plan Exercises and HW Grading

Course info
Course Title:
Instructor:
Term:
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Advanced Linear Algebra (上級線形代数)
Zeynep Yucel
2017 2nd Semester
Tue3, Tue4
2
Division of Electronic and Information System Engineering
Master's Course Students
Elective Required
English
Descripton and objective

This course intends to strengthen the mathematical background of the graduate students in computer science. We will revisit the fundamental topics in linear algebra and discuss them in a more formal manner. We will also illustrate applications on several engineering problems.
The objective of the course is to make the students gain a deeper understanding of fundamental mathematical concepts to be used in engineering applications.
Course plan
01. 2017-10-03
Basic matrix definitions and operations
Properties of matrix operations
02. 2017-10-10
Systems of linear equations
Geometric interpretation
Elementary row operations
Elimination and Substitution
Equivalent systems
03. 2017-10-17
Gaussian elimination
Gauss-Jordan method
Consistency
Linear combination
04. 2017-10-24
Row echelon form and row rank
Solutions of homogeneous systems
Null space
Nonsingular matrices
05. 2017-11-07
General form: Particular and complementary solutions
Column space
Vectors in Rnx1
Linear independence
06. 2017-11-14
Vector space
Definitions and properties
Subspaces
07. 2017-11-21
Span
Further discussion on linear independence
Basis of a vector space
08. 2017-11-28
Dimension of a vector space
Finding a basis
Coordinates and ordered of bases
09. 2017-12-05
Change of basis
Linear Transformations
10. 2018-12-12
Isomorphisim
Inverse transformation
Matrix representation of linear transformation
11. 2018-01-09
Matrix inverse
Determinants and Laplace (cofactor) expansion
Cramer’s rule
LU factorization
12. 2018-01-16
Inner product
Gram-Schmidt orthogonalization
13. 2018-01-23
Eigenvalue and eigenvectors
Cayley-Hamilton theorem
14. 2018-01-30
Diagonalization
Applications of eigenvalue and eigenvector concept
15. 2018-02-06
Brushup review
Final exercise
Exercises and HW
01. 2017-10-03
02. 2017-10-10
03. 2017-10-17
04. 2017-10-24
05. 2017-11-07
06. 2017-11-14
07. 2017-11-21
08. 2017-11-28
09. 2017-12-05
10. 2017-12-12
11. 2018-01-09
Exercise set #11  HW #05 Sol
12. 2018-01-16
Exercise set #12  HW #06
13. 2018-01-23
Exercise set #13  HW #06 Sol
14. 2018-01-30
Exercise set #14  HW #07


Grading

Homework 70%
Final exercise 30%

Each homework is graded out of 10.
HW1 HW2 HW3 HW4 HW5 HW6 HW7
43428405 9.5 8 9
43729426 9.5 10 6
43429414 10 10 6
43429415 10 10 6.5