#### Date of Award

4-21-2008

#### Degree Type

Thesis

#### Degree Name

Master of Science (MS)

#### Department

Mathematics and Statistics

#### First Advisor

Dr. Frank Hall - Co-Chair

#### Second Advisor

Dr. Zhongshan Li - Co-Chair

#### Third Advisor

Dr. Marina Arav

#### Abstract

A * sign pattern matrix* is a matrix whose entries are from the set {+,-, 0}. For a real matrix B, sgn(B) is the sign pattern matrix obtained by replacing each positive respectively, negative, zero) entry of B by + (respectively, -, 0). For a *sign pattern matrix*A, the *sign pattern class of A, denoted Q(A), is defined as { B : sgn(B)= A }. The minimum rank mr(A)(maximum rank MR(A)) of a sign pattern matrix A is the minimum (maximum) of the ranks of the real matrices in Q(A). Several results concerning sign patterns A that require almost unique rank, that is to say, the sign patterns A such that MR(A)= mr(A)+1 are established. In particular, a complete characterization of these sign patterns is obtained. Further, the results on sign patterns that require almost unique rank are extended to sign patterns A for which the spread is d =MR(A)-mr(A).*

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*#### Recommended Citation

Merid, Assefa D., "Sign Pattern Matrices That Require Almost Unique Rank." Thesis, Georgia State University, 2008.

https://scholarworks.gsu.edu/math_theses/47

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