Date of Award:
Doctor of Philosophy (PhD)
Mathematics and Statistics
LeRoy B. Beasley
Vectors and matrices over the Boolean (0,1) semiring have been studied extensively along with their applications to graph theory. The Boolean (0,1) semiring has been generalized to a class of semirings called chain semirings. This class includes the fuzzy interval. Vectors and matrices over chain semirings are examined. Rank-1 sets of vectors are defined and characterized. These rank-1 sets of vectors are then used to construct spaces of matrices (rank-1 spaces) with the property that all nonzero matrices in the space have semiring rank equal to 1. Finally, three classes of maximal (relative to containment) rank-1 spaces are identified.
Scully, Daniel Joseph, "Maximal Rank-One Spaces of Matrices Over Chain Semirings" (1988). All Graduate Theses and Dissertations. 6996.
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