Abstract
dc:description.abstract<p>Two <em>n</em> x <em>n</em> matrices A and B can make many different matrix equations, e.g., <em>AB</em> = <em>BA</em>, <em>AB</em> = <em>AA</em>, <em>ABA</em> = <em>BAB</em>, and <em>AAB</em> = <em>BAA</em>. It is not always easy to describe solutions to these matrix equations. This thesis considers the problem of describing solutions to the matrix equations <em>A</em><sup>2</sup> = <em>B</em><sup>2</sup>, <em>AB</em> = <em>A</em><sup>2</sup> and <em>AB</em> = <em>B</em><sup>2</sup>. This problem is motivated by considering the properties of commutative matrices (i.e., <em>AB</em> = <em>BA</em>), as well as the matrix form of the Yang-Baxter equation, <em>ABA</em> = <em>BAB</em>.</p> <p>For each of these equations, solutions are provided such that A ≠ B. However, in the case of <em>A</em><sup>2</sup> = <em>B</em><sup>2</sup> (when <em>A</em> has many distinct eigenvalues λ<sub>1</sub>, λ<sub>2</sub>, ... , λ<sub>k</sub> such that λ<sub>i</sub> ≠ -λ<sub>j</sub>) and in the case of <em>AB</em> = <em>A</em><sup>2</sup>, the matrices <em>A</em> and <em>B</em> must have a common eigenvector. In addition, matrices arising from graphs are considered, and restrictions are determined which impIy unique solutions to the matrix equation <em>A</em><sup>2</sup> = <em>B</em><sup>2</sup>. </p>
Degree
thesis:*- Name thesis:degree_name
- Master of Science (MS)
- Level thesis:degree_level
- Masters Thesis
- Discipline thesis:degree_discipline
- Mathematics
- Year dc:date.available
- 2013
Author and committee
dc:creator, dc:contributor.*- Author dc:creator
-
- Dangal, Thir Raj
Identifiers
dc:identifier.*- Repository record dc:identifier
- https://aquila.usm.edu/masters_theses/455
- OAI identifier oai:identifier
- oai:aquila.usm.edu:masters_theses-1522