# Course info Decription and objective Course plan Exercises and HW Grading

##### Course info

Course Title:

Instructor:

Term:

Day / Period:

Number of credits:

Classification:

Target students:

Required / elective:

Language:

Instructor:

Term:

Day / Period:

Number of credits:

Classification:

Target students:

Required / elective:

Language:

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

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.

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

Properties of matrix operations

02. 2017-10-10

Systems of linear equations

Geometric interpretation

Elementary row operations

Elimination and Substitution

Equivalent systems

Geometric interpretation

Elementary row operations

Elimination and Substitution

Equivalent systems

03. 2017-10-17

Gaussian elimination

Gauss-Jordan method

Consistency

Linear combination

Gauss-Jordan method

Consistency

Linear combination

04. 2017-10-24

Row echelon form and row rank

Solutions of homogeneous systems

Null space

Nonsingular matrices

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

Column space

Vectors in Rnx1

Linear independence

06. 2017-11-14

Vector space

Definitions and properties

Subspaces

Definitions and properties

Subspaces

07. 2017-11-21

Span

Further discussion on linear independence

Basis of a vector space

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

Finding a basis

Coordinates and ordered of bases

09. 2017-12-05

Change of basis

Linear Transformations

Linear Transformations

10. 2018-12-12

Isomorphisim

Inverse transformation

Matrix representation of linear transformation

Inverse transformation

Matrix representation of linear transformation

11. 2018-01-09

Matrix inverse

Determinants and Laplace (cofactor) expansion

Cramer’s rule

LU factorization

Determinants and Laplace (cofactor) expansion

Cramer’s rule

LU factorization

12. 2018-01-16

Inner product

Gram-Schmidt orthogonalization

Gram-Schmidt orthogonalization

13. 2018-01-23

Eigenvalue and eigenvectors

Cayley-Hamilton theorem

Diagonalization

Cayley-Hamilton theorem

Diagonalization

14. 2018-01-30

Applications of eigenvalue and eigenvector concept

Markov chains

Singular value decomposition

Markov chains

Singular value decomposition

15. 2018-02-06

Brushup review

Final exercise

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

12. 2018-01-16

13. 2018-01-23

14. 2018-01-30

##### Grading

Homework 70%

Final exercise 30%

Each homework is graded out of 10 points and the final exerise is graded out of 30 points.

Final exercise 30%

Each homework is graded out of 10 points and the final exerise is graded out of 30 points.

H1 | H2 | H3 | H4 | H5 | H6 | H7 | Final | Tot | |

43428405 | 9.5 | 8 | 9 | 7 | 10 | 9.5 | 9 | 30 | 92 |

43729426 | 9.5 | 10 | 6 | 7 | 10 | 10 | 10 | 30 | 92.5 |

43429414 | 10 | 10 | 6 | 7 | 10 | 10 | 10 | 30 | 93 |

43429415 | 10 | 10 | 6.5 | 7 | 10 | 9.5 | 9 | 30 | 92 |