Dissertation
Semimonotone Matrices
Doctor of Philosophy (PhD), Washington State University
01/2020
Handle:
https://hdl.handle.net/2376/117860
Abstract
Semimonotone matrices $A$ are those real matrices for which the operation $Ax$ does not negate all positive entries of any nonzero, entrywise nonnegative vector $x$. Semimonotone matrices play an important role in the linear complementarity problem and have connections with a variety of other matrix classes. In this thesis, properties of semimonotone matrices are reviewed and developed. The problem of construction and detection is explored and discussed, although finding an efficient detection and construction algorithm remains an open problem. To get closer toward finding a characterization that would allow one to develop such an algorithm, the almost semimonotone matrices are studied. Finally, (strict) central matrices and their connections to semimonotone matrices are explored.
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Details
- Title
- Semimonotone Matrices
- Creators
- Megan Wendler
- Contributors
- Michael J Tsatsomeros (Advisor)Judith J McDonald (Committee Member)Nikolaos Voulgarakis (Committee Member)
- Awarding Institution
- Washington State University
- Academic Unit
- Mathematics and Statistics, Department of
- Theses and Dissertations
- Doctor of Philosophy (PhD), Washington State University
- Number of pages
- 104
- Identifiers
- 99900581703301842
- Language
- English
- Resource Type
- Dissertation