ECTS @ IUE ECTS @ IUE ECTS @ IUE ECTS @ IUE ECTS @ IUE ECTS @ IUE ECTS @ IUE

Syllabus ( MATH 451 )


   Basic information
Course title: Matrix Theory
Course code: MATH 451
Lecturer: Prof. Dr. Sibel ÖZKAN
ECTS credits: 5
GTU credits: 2 (3+0+0)
Year, Semester: 4, Fall and Spring
Level of course: First Cycle (Undergraduate)
Type of course: Departmental Elective
Language of instruction: English
Mode of delivery: Face to face
Pre- and co-requisites: None
Professional practice: No
Purpose of the course: The course helps the student to understand the unifying concepts of Matris theory and provides an area of mathematics that proved to be useful in other areas.
   Learning outcomes Up

Upon successful completion of this course, students will be able to:

  1. List the unifying concepts of Matris theory

    Contribution to Program Outcomes

    1. Having the knowledge about the scope, applications, history, problems, and methodology of mathematics that are useful to humanity both as a scientific and as an intellectual discipline.
    2. Describing, formulating, and analyzing real-life problems using mathematical and statistical techniques.
    3. Having improved abilities in mathematics communications, problem-solving, and brainstorming skills.

    Method of assessment

    1. Written exam
  2. Apply an special area of mathematics to other areas

    Contribution to Program Outcomes

    1. Having the knowledge about the scope, applications, history, problems, and methodology of mathematics that are useful to humanity both as a scientific and as an intellectual discipline.
    2. Having improved abilities in mathematics communications, problem-solving, and brainstorming skills.
    3. Exhibiting professional and ethical responsibility.

    Method of assessment

    1. Written exam
  3. Use canonical forms

    Contribution to Program Outcomes

    1. Having the knowledge about the scope, applications, history, problems, and methodology of mathematics that are useful to humanity both as a scientific and as an intellectual discipline.
    2. Having improved abilities in mathematics communications, problem-solving, and brainstorming skills.

    Method of assessment

    1. Written exam
   Contents Up
Week 1: Matris algebra; Matris addition and multiplication
Week 2: Special types of matrices, partioned matrices, Echelon form of a matris
Week 3: Elementary matrices, Inverse of a matris.
Week 4: Determinants, Properties of determinants, Cramers rule
Week 5: Vector spaces: Linear independence Basis, dimension
Week 6: Linear transformations, Kernel and Range, nullity
Week 7: Matris of a Linear Transformations, rank of matris
Week 8: Systems of linear equations: Gaussian elimination, Gauss-Jordan reduction method-midterm exam
Week 9: Characteristic and minimum polynomial, Eigenvalues and eigenvectors, diagonalization
Week 10: Inner product spaces, Cauchy-Bunyakowstky inequality
Week 11: Ortagonal transforms, Gram-Schmidt Process
Week 12: Annihilating Polynomials of Matrices , Special Types of Matrices: Idempotence,
Nilpotence, Involution, and Projection
Week 13: Positive Definite Matrices and Positive Semidefinite Matrices
Week 14: Vector and matris norms
Week 15*: -
Week 16*: Final exam
Textbooks and materials: Matrix theory by David W. Lewis
Recommended readings: Matrix theory by David W. Lewis

Elementary Lineer Algebra 7th Ed. Bernard Kolman ve David R. Hill
  * Between 15th and 16th weeks is there a free week for students to prepare for final exam.
Assessment Up
Method of assessment Week number Weight (%)
Mid-terms: 8 40
Other in-term studies: 0
Project: 0 0
Homework: 0
Quiz: 0
Final exam: 16 60
  Total weight:
(%)
   Workload Up
Activity Duration (Hours per week) Total number of weeks Total hours in term
Courses (Face-to-face teaching): 3 14
Own studies outside class: 4 14
Practice, Recitation: 0 0
Homework: 0 0
Term project: 0 0
Term project presentation: 1 1
Quiz: 0 0
Own study for mid-term exam: 8 1
Mid-term: 2 1
Personal studies for final exam: 10 1
Final exam: 2 1
    Total workload:
    Total ECTS credits:
*
  * ECTS credit is calculated by dividing total workload by 25.
(1 ECTS = 25 work hours)
-->