Information Package / Course Catalogue
Linear Algebra III
Course Code: MAT407
Course Type: Area Elective
Couse Group: First Cycle (Bachelor's Degree)
Education Language: Turkish
Work Placement: N/A
Theory: 2
Prt.: 2
Credit: 3
Lab: 0
ECTS: 6
Objectives of the Course

The aim of this course is to introduce students to some special types of complex matrices such as normal matrices, Hermitian matrices, unitary matrices and to give them the ability to explain the algebraic differences and similarities between them. In addition, the aim of this course is to help students learn some special types of (linear) operators defined on inner product spaces and the basic properties of their adjoints.

Course Content

Normal and Hermitian matrices, Unitary matrices, Unitary diagonalization of complex square matrices, Real symmetric matrices and orthogonal matrices, Real quadratic forms, Norm and its properties in inner product spaces, Orthogonal and orthonormal sets, Linear operators and their adjoints in inner product spaces, Normal operators, Hermitian operators, Unitary operators.

Name of Lecturer(s)
Lec. Berna ARSLAN
Learning Outcomes
1.To be able to decide whether a given matrix is a normal, Hermitian or unitary matrix and to give examples of these matrices.
2.To be able to explain the relationship between Hermitian, unitary and normal matrices.
3.To be able to determine the type of cone sections in the plane through real quadratic forms.
4.To understand Hermitian, unitary and normal operators and to give examples of these operators.
5.To be able to interpret the relationships between the mathematical concepts learned.
Recommended or Required Reading
1.Topics in Linear Algebra, Koç, C., Doğuş University, Ankara, 2010.
2.Linear Algebra, Hoffman, K. M., Kunze, R. A., Printice Hall, 2. Edition, 1971.
3.Elementary Linear Algebra, Anton, H., Kaul, A., Wiley&Sons, Inc., 12. Edition, 2019.
4.Introductory Linear Algebra with Applications, Kolman, B., Hill, D. R., Printice Hall, 7. Edition, 2001.
Weekly Detailed Course Contents
Week 1 - Theoretical & Practice
The conjugate transpose of complex matrices and Normal matrices
Week 2 - Theoretical & Practice
Properties of normal matrices
Week 3 - Theoretical & Practice
Hermitian matrices and diagonalizability of Hermitian matrices
Week 4 - Theoretical & Practice
The concept of norm in an inner product space and its properties, Orthogonal and orthonormal sets and bases
Week 5 - Theoretical & Practice
Unitary matrices and their properties
Week 6 - Theoretical & Practice
Unitary diagonalization of complex square matrices
Week 7 - Theoretical & Practice
Real symmetric matrices and orthogonal matrices
Week 8 - Theoretical & Practice
Diagonalization of real symmetric matrices (Midterm)
Week 9 - Theoretical & Practice
Real quadratic forms
Week 10 - Theoretical & Practice
Positive definite quadratic forms
Week 11 - Theoretical & Practice
Linear maps and their adjoints on inner product spaces
Week 12 - Theoretical & Practice
Eigenvalues of normal operators and their extensions
Week 13 - Theoretical & Practice
Hermitian operators
Week 14 - Theoretical & Practice
Unitary operators
Assessment Methods and Criteria
Type of AssessmentCountPercent
Midterm Examination1%40
Final Examination1%60
Workload Calculation
ActivitiesCountPreparationTimeTotal Work Load (hours)
Lecture - Theory141242
Lecture - Practice140228
Individual Work140342
Midterm Examination116218
Final Examination118220
TOTAL WORKLOAD (hours)150
Contribution of Learning Outcomes to Programme Outcomes
PÇ-1
PÇ-2
PÇ-3
PÇ-4
PÇ-5
PÇ-6
PÇ-7
PÇ-8
PÇ-9
PÇ-10
PÇ-11
PÇ-12
PÇ-13
PÇ-14
PÇ-15
PÇ-16
PÇ-17
PÇ-18
OÇ-1
2
2
3
OÇ-2
3
2
3
2
OÇ-3
3
3
3
3
4
OÇ-4
4
5
4
4
4
OÇ-5
3
5
2
2
4
3
2
Adnan Menderes University - Information Package / Course Catalogue
2026