#### 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