At the end of this course, the students; 1) will have learned canonical matrix representations of linear operators on finite dimensional vector spaces over arbitrary fields.
MODE OF DELIVERY
Face to face
PRE-REQUISITES OF THE COURSE
No
RECOMMENDED OPTIONAL PROGRAMME COMPONENT
There is no recommended optional programme component for this course.
COURSE DEFINITION
Matrices and determinants. Systems of linear equations. Vector spaces, bases and dimensions. Linear transformations, change of bases. Inverses of a linear transformations. Isomorphism. Eigenvalues and eigen vectors, Jordan normal form. İnner and cross products, orthogonality, quadratic forms, normed spaces
COURSE CONTENTS
WEEK
TOPICS
1st Week
Eigenvalues and Eigenvectors
2nd Week
Diagonalization
3rd Week
Normal form of Polynomial matrices.
4th Week
Equivalence of Characteristic Matrices and Similarity.
5th Week
Rational and Jordan Canonical Forms.
6th Week
Diagonalizable Complex Matrices.
7th Week
Real Symmetric Matrices,Hermitian Matrices,Positive Matrices.
8th Week
MIDTERM
9th Week
Unitary and Orthogonal Matrices,Reduction of Quadratic Forms,Orthogonal Similarity.
10th Week
İner products,Norm and Orthogonality,Matrix Forms of İner Products.
11th Week
Orthogonal and Orthonormal Bases. Orthogonal Projections.
12th Week
The Gram - Schmidt Orthogonalization Process. The Method of Least Squares.
13th Week
Linear operators and their adjoints on İnner Product Spaces.
14th Week
Linear Functionals on İnner Product Spaces.
RECOMENDED OR REQUIRED READING
Topics in Linear Alcebra
PLANNED LEARNING ACTIVITIES AND TEACHING METHODS
Lecture,Problem Solving,Questions/Answers
ASSESSMENT METHODS AND CRITERIA
Quantity
Percentage(%)
Mid-term
1
30
Assignment
1
10
Project
1
10
Total(%)
50
Contribution of In-term Studies to Overall Grade(%)
50
Contribution of Final Examination to Overall Grade(%)
50
Total(%)
100
LANGUAGE OF INSTRUCTION
Turkish
WORK PLACEMENT(S)
No
KEY LEARNING OUTCOMES (KLO) / MATRIX OF LEARNING OUTCOMES (LO)
