Orthogonal Decompositions of Traceless Matrix Spaces
(2019) In Master’s Theses in Mathematical Sciences FMAM05 20191Mathematics (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.
Please use this url to cite or link to this publication:
http://lup.lub.lu.se/student-papers/record/8978380
- author
- Olsson, Patrik LU
- supervisor
- organization
- course
- FMAM05 20191
- year
- 2019
- 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
- date added to LUP
- 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}}, }