# LUP Student Papers

## LUND UNIVERSITY LIBRARIES

### Orthogonal Decompositions of Traceless Matrix Spaces

(2019) In Master’s Theses in Mathematical Sciences FMAM05 20191
Mathematics (Faculty of Engineering)
Abstract
We study orthogonal decompositions of complex special linear Lie algebras or, in other words, linear spaces consisting of complex matrices with zero trace. The conjugacy of the component subspaces give rise to change of basis matrices with a particular form that we, for the moment, call "nice". We prove a necessary and sufficient condition for this form, which allows us to characterize orthogonal decompositions as a finite set of matrices: namely, the change of basis matrices from the standard diagonal component subspace to each of the other \$n\$ component subspaces. We develop a basic theory for nice matrices, and then present methods to construct known orthogonal decompositions in terms of the aforementioned characterization of them.
author
supervisor
organization
course
FMAM05 20191
year
type
H2 - Master's Degree (Two Years)
subject
publication/series
Master’s Theses in Mathematical Sciences
report number
LUTFMA-3379-2019
ISSN
1404-6342
other publication id
2019:E17
language
English
id
8978380
2019-07-16 13:42:19
date last changed
2019-07-16 13:42:19
```@misc{8978380,
abstract     = {{We study orthogonal decompositions of complex special linear Lie algebras or, in other words, linear spaces consisting of complex matrices with zero trace. The conjugacy of the component subspaces give rise to change of basis matrices with a particular form that we, for the moment, call "nice". We prove a necessary and sufficient condition for this form, which allows us to characterize orthogonal decompositions as a finite set of matrices: namely, the change of basis matrices from the standard diagonal component subspace to each of the other \$n\$ component subspaces. We develop a basic theory for nice matrices, and then present methods to construct known orthogonal decompositions in terms of the aforementioned characterization of them.}},
author       = {{Olsson, Patrik}},
issn         = {{1404-6342}},
language     = {{eng}},
note         = {{Student Paper}},
series       = {{Master’s Theses in Mathematical Sciences}},
title        = {{Orthogonal Decompositions of Traceless Matrix Spaces}},
year         = {{2019}},
}

```