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Dissertation
Factorizations of Copositive Matrices and the Copositive Range
Doctor of Philosophy (PhD), Washington State University
2025
Abstract
Copositive matrices, first introduced by Theodore S. Motzkin in 1952, are generalizations of positive semidefinite matrices. A real symmetric matrix A ∈ Mn(R) is called copositive if xT Ax ≥ 0 for all x ≥ 0. The study of copositivity has expanded into various areas of mathematics, including optimization, graph theory, and game theory. In this dissertation, we present several preliminary results on copositive matrices, including cone properties and copositivity preservers. Additionally, we present new results on factorizations of copositive matrices and introduce the concept of the copositive range, providing several findings related to its structure and properties.
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Details
- Title
- Factorizations of Copositive Matrices and the Copositive Range
- Creators
- Seong Jun Park
- Contributors
- Michael Tsatsomeros (Advisor)Judith McDonald (Committee Member)Sergey Lapin (Committee Member)
- Awarding Institution
- Washington State University
- Academic Unit
- Department of Mathematics and Statistics
- Theses and Dissertations
- Doctor of Philosophy (PhD), Washington State University
- Number of pages
- 80
- Identifiers
- 99901357897901842
- Language
- English
- Resource Type
- Dissertation