Date of Award
5-3-2007
Degree Type
Thesis
Degree Name
Master of Science (MS)
Department
Mathematics and Statistics
First Advisor
Dr. Frank J. Hall - Chair
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.
Recommended Citation
Demir, Nilay Sezin, "Spectrally Arbitrary and Inertially Arbitrary Sign Pattern Matrices." Thesis, Georgia State University, 2007.
https://scholarworks.gsu.edu/math_theses/26