Ph.D. Tezi Görüntüleme | |||||||||||||||||||||
|
|
||||||||||||||||||||
| Summary: In this thesis, the following main results have been obtained: 1) Let H:C^n→R^2n be the natural linear operator from the n-dimensional C^n complex vector space to the 2n-dimensional R^2n real vector space. For an arbitrary linear transformation F:C^n→C^n, the relation between the determinants det(F) and det(HF(H^(-1))) is found.2) In the n-dimensional unitary space, an arbitrary isometry is a composition of a translation and a real unitary transformation. 3) Let G be the unitary group or the group of all isometries of C^n. In the n-dimensional unitary space, complete systems of G-invariants have been obtained for finite subsets of C^n. The minimality properties of these complete systems of G-invariants have been proved.
Key Words: Unitary Geometry, Unitary Group, Invariants, Isometries | |||||||||||||||||||||