Course info Contact info Description and objective Course plan

Course info
Course Title:

Course number:
Instructor:
Term:
Day / Period:
Number of credits:
Target students:
Required / elective:
Language:
Advanced Linear Algebra
上級線形代数
432116
Zeynep Yucel
1st and 2th terms
1st Term Tue3, Tue4, 2nd Term Mon1, Mon2
2
Graduate (M1,M2)
Elective Required
English
Contact info
Zeynep Yucel
Room:
Tel:
E-mail:

Engineering building no. 4 Room-703
086-251-8176 (Internal 8176)
mailAddress
Description 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.
Basic matrix definitions
Matrix operations
02.
Systems of linear equations
Geometric interpretation
Elementary row operations
Elimination and Substitution
Equivalent systems
03.
Gaussian elimination
Gauss-Jordan method
Consistency
Linear combination
04.
Row echelon form and row rank
Solutions of homogeneous systems
Null space
Nonsingular matrices
05.
Particular and complementary
solutions
Column space
Vectors in Rnx1
Linear independence
06.
Vector space
Definitions and properties
Subspaces
07.
Span
Further discussion on
linear independence
Basis of a vector space
08.
Dimension of a vector space
Finding a basis
Coordinates and ordered of bases
09.
Change of basis
Linear Transformations
10.
Isomorphisim
Inverse transformation
Matrix representation
of linear transformations
11.
Determinants and matrix inverse
Laplace (cofactor) expansion
Cramer’s rule
LU factorization
12.
Inner product
Gram-Schmidt orthogonalization
13.
Eigenvalue and eigenvectors
Cayley-Hamilton theorem
Diagonalization
14.
Applications of eigenvalue
and eigenvectors
Markov chains
Singular value decomposition
15.
Brushup review
Final exercise