The geometry of matrices and linear preserver problems

01.10.2007 - 30.09.2008
Research funding project
The aim of the project is to study the projective and affine geometry of matrices and the related questions in the research field of linear preserver problems. In the geometry of matrices, there are four kinds of matrices first studied by L. K. Hua: the symmetric, Hermitian, alternate, and rectangular matrices. The aim of the study is to characterize the group of motions by as few geometric invariants as possible. For example, Hua found that the invariant adjacency is sufficient to characterize the basic group. This statement is called the fundamental theorem of the geometry of matrices. The fundamental theorem of the geometry of matrices can be applied to linear preserver problems. Linear preservers are linear maps on linear spaces of matrices that leave certain properties or relations invariant. There are various other research fields which are connected to the geometry of matrices, e.g., Laguerre geometry, special relativity, ring geometry, and polar spaces. We are going to study the following questions: 1. Fundamental theorem of geometry of alternate matrices and application to linear preserver problems. 2. Distance k preserver problems. 3. Adjacency preserver problems between two different spaces. 4. Quasi-commutativity preserver problems.

People

Project leader

Sub project leader

Institute

Grant funds

  • FWF - Österr. Wissenschaftsfonds (National) Austrian Science Fund (FWF)

Research focus

  • Beyond TUW-research focus: 100%

Keywords

GermanEnglish
Geometrie der MatrizenGeometry of matrices
Linear Preserver ProblemeLinear Preserver Problems
Adjazenztreue AbbildungenAdjacency preserving mappings
Rang-k-treue AbbildungenRank-k-preserving mappings
Duale polare RäumeDual polar spaces

Publications