Type of Document Master's Thesis Author Merid, Assefa D Author's Email Address efamerid@msn.com URN etd-04182008-132138 Title Sign Pattern Matrices That Require Almost Unique Rank Degree Master of Science Department Mathematics and Statistics Advisory Committee
Advisor Name Title Dr. Frank Hall Committee Co-Chair Dr. Zhongshan Li Committee Co-Chair Dr. Marina Arav Committee Member Keywords
- Minimum rank
- Sign pattern matrix
- Maximum rank
- L-matrix
- Requires unique rank
- Spread
- Requires almost unique rank
Date of Defense 2008-04-11 Availability unrestricted 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 matrixA, 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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