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/studentpapers/record/8978380
 author
 Olsson, Patrik ^{LU}
 supervisor

 Victor Ufnarovski ^{LU}
 organization
 course
 FMAM05 20191
 year
 2019
 type
 H2  Master's Degree (Two Years)
 subject
 publication/series
 Master’s Theses in Mathematical Sciences
 report number
 LUTFMA33792019
 ISSN
 14046342
 other publication id
 2019:E17
 language
 English
 id
 8978380
 date added to LUP
 20190716 13:42:19
 date last changed
 20190716 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 = {{14046342}}, language = {{eng}}, note = {{Student Paper}}, series = {{Master’s Theses in Mathematical Sciences}}, title = {{Orthogonal Decompositions of Traceless Matrix Spaces}}, year = {{2019}}, }