Dissertation
Spectrally arbitrary zero-nonzero patterns
Washington State University
Doctor of Philosophy (PhD), Washington State University
05/2009
DOI:
https://doi.org/10.7273/000005651
Abstract
This thesis establishes a complete list of all 3 3 and 4 4 complex spectrally arbitrary zero-nonzero patterns. Highlighted in this list are important examples of irreducible complex spectrally arbitrary zero-nonzero patterns which fail to satisfy the Nilpotent-Jacobian condition. Examples of complex spectrally arbitrary zero-nonzero patterns whose corresponding directed graph does not contain a two-cycle are illustrated in Chapter 3. In Chapter 4 the minimum number of nonzero entries contained in an irreducible zero-nonzero pattern that guarantees the pattern is spectrally arbitrary is determined. Illustrated in Chapter 5 is the reduction of this number of nonzero entries contained in a irreducible zero-nonzero pattern A, when exactly one transversal is contained in an irreducible subpattern of A. Lastly, future work in the area of spectrally arbitrary patterns is described in Chapter 6.
Metrics
4 File views/ downloads
25 Record Views
Details
- Title
- Spectrally arbitrary zero-nonzero patterns
- Creators
- Amy Ann Yielding
- Contributors
- Judith Joanne McDonald (Chair)Matthew G Hudelson (Committee Member) - Washington State University, Department of Mathematics and StatisticsMichael Tsatsomeros (Committee Member) - Washington State University, Department of Mathematics and Statistics
- Awarding Institution
- Washington State University
- Academic Unit
- Department of Mathematics and Statistics
- Theses and Dissertations
- Doctor of Philosophy (PhD), Washington State University
- Publisher
- Washington State University
- Number of pages
- 92
- Identifiers
- 99901054739201842
- Language
- English
- Resource Type
- Dissertation