# Linear Algebra II (MATH232) Course Detail

Course Name Course Code Season Lecture Hours Application Hours Lab Hours Credit ECTS
Linear Algebra II MATH232 4. Semester 4 0 0 4 7
Pre-requisite Course(s)
Math 231 Linear Algebra I
Course Language English Compulsory Departmental Courses Bachelor’s Degree (First Cycle) Lecture, Question and Answer, Drill and Practice. Being a continuation of Math 231, the aim is to introduce the students to the very heart of the subject including topics such as inner product spaces and linear mappings on them, canonical (diagonal, triangular, Jordan, and rational) matrix forms of linear mappings, bilinear and quadratic forms. The students who succeeded in this course; understand the basics of inner product spaces, decompose a vector space as a direct sum of its subspaces, obtain special types of matrices representing a given linear map, understand and find eigenvalues and eigenvectors, determine if a matrix is diagonalizable, and if it is, diagonalize it, find bases for eigenspaces, find bases for dual space of a vector space, understand fundamentals of bilinear and quadratic forms. Eigenvalues and eigenvectors, elementary canonical forms, the rational and Jordan forms, inner product spaces, operators on Inner product spaces, bilinear forms.

### Weekly Subjects and Releated Preparation Studies

Week Subjects Preparation
1 Division in a Polynomial Ring, Prime Factorization, Factorization of Polynomials over C and R pp. 1-17
2 Ideals, Matrices over Polynomials, Characteristic Polynomial and Minimal Polynomial pp. 18-40
3 Eigenvalues and Eigenvectors, Diagonalization. pp. 41-52
4 Normal Form of Polynomial Matrices, Equivalence of Characteristic Matrices and Similarity pp. 66-81
5 Rational and Jordan Canonical forms pp. 82-102
6 Normal Matrices, Real Symmetric Matrices pp. 104-118
7 Hermitian Matrices, Positive Matrices, Standard Inner Products pp. 119-132, 137-141
8 Unitary and Orthogonal Matrices, Reduction of Quadratic Forms, Orthogonal Similarity pp. 142-160
9 Inner products, Norm and Orthogonality pp. 162-178
10 Matrix Forms of Inner Products, Orthogonal and Orthonormal Basis, Orthogonal Projections pp. 179-192
11 The Gram-Schmidt Orthogonalization process pp. 193-194
12 Linear Operators and Their Adjoints on Inner Product Spaces, Normal Operators, Unitary Operators, Orthogonal Operators. pp. 203-211
13 Linear Functionals on Inner Product Spaces pp. 212-220
14 Bilinear Forms
15 General Review
16 Final Exam

### Sources

Course Book 1. Topics in Linear Algebra, Cemal Koç, Doğuş University, Ankara, 2010 2. T. S. Blyth and E. F. Robertson, Further Linear Algebra, Springer-Verlag, London, 2002. 3. K. Hoffman and R. Kunze, Linear Algebra, 2nd Edition, Prentice-Hall, New Jersey, 1971. 4. T.S. Blyth and E.F. Robertson, Basic Linear Algebra, 2nd Edition, Springer-Verlag, London, 2002. 5. B. Kolman and D. R. Hill, Elementary Linear Algebra, 9th Edition, Prentice-Hall, New Jersey, 2008.

### Evaluation System

Attendance/Participation - -
Laboratory - -
Application - -
Field Work - -
Special Course Internship - -
Quizzes/Studio Critics - -
Homework Assignments 5 10
Presentation - -
Project - -
Report - -
Seminar - -
Midterms Exams/Midterms Jury 2 55
Final Exam/Final Jury 1 35
Toplam 8 100
 Percentage of Semester Work 65 35 100

### Course Category

Core Courses X

### The Relation Between Course Learning Competencies and Program Qualifications

# Program Qualifications / Competencies Level of Contribution
1 2 3 4 5
1 Has the ability to apply scientific knowledge gained in the undergraduate education and to expand and extend knowledge in the same or in a different area X
2 Can apply gained knowledge and problem solving abilities in inter-disciplinary research X
3 Has the ability to work independently within research area, to state the problem, to develop solution techniques, to solve the problem, to evaluate the obtained results and to apply them when necessary X
4 Takes responsibility individually and as a team member to improve systematic approaches to produce solutions in unexpected complicated situations related to the area of study X
5 Can develop strategies, implement plans and principles on the area of study and can evaluate obtained results within the framework X
6 Can develop and extend the knowledge in the area and to use them with scientific, social and ethical responsibility X
7 Has the ability to follow recent developments within the area of research, to support research with scientific arguments and data, to communicate the information on the area of expertise in a systematically by means of written report and oral/visual presentation X
8 To have an oral and written communication ability in at least one of the common foreign languages ("European Language Portfolio Global Scale", Level B2) X
9 Has software and hardware knowledge in the area of expertise, and has proficient information and communication technology knowledge X
10 Follows scientific, cultural, and ethical criteria in collecting, interpreting and announcing data in the research area and has the ability to teach. X
11 Has professional ethical consciousness and responsibility which takes into account the universal and social dimensions in the process of data collection, interpretation, implementation and declaration of results in mathematics and its applications. X

Activities Number Duration (Hours) Total Workload
Course Hours (Including Exam Week: 16 x Total Hours)
Laboratory
Application
Special Course Internship
Field Work
Study Hours Out of Class
Presentation/Seminar Prepration
Project
Report
Homework Assignments
Quizzes/Studio Critics
Prepration of Midterm Exams/Midterm Jury 2 14 28
Prepration of Final Exams/Final Jury