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Sign Pattern Matrices That Require Almost Unique Rank

Merid, Assefa D
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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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Date
2008-04-21
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Research Projects
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Keywords
Minimum rank, Sign pattern matrix, Maximum rank, L-matrix, Requires unique rank, Spread, Requires almost unique rank
Citation
Merid, Assefa D. "Sign Pattern Matrices That Require Almost Unique Rank." 2008. Thesis, Georgia State University. https://doi.org/10.57709/1059703
Embargo Lift Date
2012-01-26
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