PAÜ .:. Eğitim Öğretim Bilgi Sistemi

COURSE INFORMATION

Course Code	Course Title	L+P Hour	Semester	ECTS
IMO 2004	LINEAR ALGEBRA 2	2 + 0	4th Semester	2

COURSE DESCRIPTION

Course Level	Bachelor's Degree
Course Type	Compulsory
Course Objective	The aim is for students to understand the concepts of orthogonalization and distance functions in vector spaces, to be able to perform determinant operations, to find solutions to systems of linear equations using determinants, and to understand diagonalization operations in matrices.
Course Content	The concept of orthogonality and distance function, Gram-Schmidt process, orthogonal matrices, Determinants; determinants and reduction, solving systems of linear equations by Cramer’s rule. Characteristic polynomial, eigenvalues, and eigen vectors, diagonalization in matrices.
Prerequisites	No the prerequisite of lesson.
Corequisite	No the corequisite of lesson.

COURSE LEARNING OUTCOMES

1	Knows the concept of the inner product space.
2	Knows how to transform a vector set into an orthogonal form using the Gram-Schmidt method.
3	Explains the relationship between the inner product space and the normed vector space.
4	Calculates the determinant of a matrix using cofactors.
5	Uses Cramer's method in solving systems of linear equations.
6	Calculates the characteristic polynomial of the given matrix
7	Finds the eigenvalues and eigenvectors of a matrix.
8	Knows how to obtain the diagonalized form of a matrix.
9	Explains the geometric relationship between quadratic forms and diagonalization.
10	alculates the minimum polynomial of a matrix.

COURSE'S CONTRIBUTION TO PROGRAM

	PO 01	PO 02	PO 03	PO 04	PO 05	PO 06	PO 07	PO 08	PO 09	PO 10	PO 11	PO 12	PO 13	PO 14
LO 001	4	4	3	3	4	4	4	4	4	5	4	4	5	5
LO 002	4	4	3	3	4	4	4	4	4	5	4	4	5	5
LO 003	4	4	3	3	4	4	4	4	4	5	4	4	5	5
LO 004	4	4	3	3	4	4	4	4	4	5	4	4	5	5
LO 005	4	4	3	3	4	4	4	4	4	5	4	4	5	5
LO 006	4	4	3	3	4	4	4	4	4	5	4	4	5	5
LO 007	4	4	3	3	4	4	4	4	4	5	4	4	5	5
LO 008	4	4	3	3	4	4	4	4	4	5	4	4	5	5
LO 009	4	4	3	3	4	4	4	4	4	5	4	4	5	5
LO 010	4	4	3	3	4	4	4	4	4	5	4	4	5	5
Sub Total	40	40	30	30	40	40	40	40	40	50	40	40	50	50
Contribution	4	4	3	3	4	4	4	4	4	5	4	4	5	5

ECTS ALLOCATED BASED ON STUDENT WORKLOAD BY THE COURSE DESCRIPTION

Activities	Quantity	Duration (Hour)	Total Work Load (Hour)
Course Duration (14 weeks/theoric+practical)	14	2	28
Hours for off-the-classroom study (Pre-study, practice)	7	1	7
Mid-terms	1	7	7
Final examination	1	10	10
Total Work Load ECTS Credit of the Course			52 2

COURSE DETAILS

Select Year

Course Details

Course Code	Course Title	L+P Hour	Course Code	Language Of Instruction	Course Semester	Mode of Delivery
IMO 2004	LINEAR ALGEBRA 2	2 + 0	1	Turkish	2025-2026 Spring	Face to Face

Course Coordinator	E-Mail	Phone Number	Course Location	Attendance
Prof. Dr. İSMET AYHAN	iayhan@pau.edu.tr		EGT A0232-03	%

Goals		The aim is for students to understand the concepts of orthogonalization and distance functions in vector spaces, to be able to perform determinant operations, to find solutions to systems of linear equations using determinants, and to understand diagonalization operations in matrices.
Content		The concept of orthogonality and distance function, Gram-Schmidt process, orthogonal matrices, Determinants; determinants and reduction, solving systems of linear equations by Cramer’s rule. Characteristic polynomial, eigenvalues, and eigen vectors, diagonalization in matrices.

Topics

Weeks	Topics
1	İnner Product space and The Distance Function
2	Cauchy-Schwarz inequality and applications
3	Orthogonal bases and projections
4	The Gram-Schmidt Process for constructing an ortogonal/ortonormal basis for an inner product space
5	Vector Spaces with Norm
6	The Determinant Function and their properties
7	The Cofaktor Methot for computing determinants
8	Using Row reduction to find determinants
9	The Midterm Exam
10	By using the Cramer Rule,solving the system of Linear Equations
11	The Characteristic Equation of a matrix, Eigenvalues and Eigenvectors
12	Diagonalization
13	Diagonalizations of The Real Symmetric Matrices and Quadratic Forms
14	The Minumum Polinom of a matrix

Materials

Materials are not specified.

Resources

Resources	Resources Language
Seymur Lipschuts, (Çev):Prof Dr H Hilmi Hacısalihoğlu, Lineer Cebir	Türkçe

Course Assessment

Assesment Methods	Percentage (%)	Assesment Methods Title
Final Exam	60	Final Exam
Midterm Exam	40	Midterm Exam

L+P: Lecture and Practice
PQ: Program Learning Outcomes
LO: Course Learning Outcomes

Prospective Student