M.Sc. Tezi Görüntüleme

Student:	Hüsnü Anıl ÇOBAN
Supervisor:	Prof.Dr.Djavvat KHADJİEV
Department:	Matematik
Institution:	Graduate School of Natural and Applied Sciences
University:	Karadeniz Technical University, Turkey

Title of the Thesis:	Transformation Groups in Unitary
Level:	M.Sc.
Acceptance Date:	10/7/2008
Number of Pages:	106
Registration Number:	i1934

Summary:

In this thesis, the following questions on unitary spaces of 1 and 2 dimensions are studied.

These are :

1. The concepts of a real linear transformation in a complex vector space has been given. A correlation between a real linear transformation and a complex linear transformation has been found.

2. Concepts of real unitary and imaginary unitary real linear transformations are given. A connection between these concepts and unitary transformation is investigated.

3. Correlations between isometries in the n-dimensional unitary space (n = 1, 2) and isometries in the 2n-dimensional real Euclidean space (n = 1, 2) have been studied.

4. It has been proved that the intersection of the group of 2n-dimensional orthogonal transformations and the group of 2n-dimensional symplectic transformations is equal to the group of n-dimensional unitary transformations for n = 1, 2.

Key Words: Linear Transformation, Unitary Group, Isometry