Type of Document Master's Thesis Author Demir, Nilay Sezin Author's Email Address nilsezindemir@yahoo.com URN etd-04192007-133653 Title Spectrally Arbitrary and Inertially Arbitrary Sign Pattern Matrices Degree Master of Science Department Mathematics and Statistics Advisory Committee
Advisor Name Title Dr. Frank J. Hall Committee Chair Keywords
- potentially stable pattern
- sign pattern matrix
- spectrally arbitrary pattern
- grobner basis
- inertially arbitrary pattern
- potentially nilpotent pattern
- tree sign pattern
Date of Defense 2007-03-02 Availability unrestricted Abstract A sign pattern(matrix) is a matrix whose entries are from the set {+,-,0}. An n x n sign pattern matrix is a spectrally arbitrary pattern(SAP) if for every monic real polynomial p(x) of degree n, there exists a real matrix B whose entries agree in sign with A such that the characteristic polynomial of B is p(x). An n x n pattern A is an inertialy arbitrary pattern(IAP) if (r,s,t) belongs to the inertia set of A for every nonnegative triple (r,s,t) with r+s+t=n. Some elementary results on these two classes of patterns are first exhibited. Tree sign patterns are then investigated, with a special emphasis on 4 x 4 tridiagonal sign patterns. Connections between the SAP(IAP) classes and the classes of potentially nilpotent and potentially stable patterns are explored. Some interesting open questions are also provided.Files
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