Nonnegative rank-preserving operators |
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Authors: | LeRoy B Beasley David A Gregory Norman J Pullman |
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Institution: | Mathematics Department Utah State University Logan, Utah 84322, USA;Department of Mathematics and Statistics Queen''s University Kingston, Ontario, Canada, K7L 3N6 |
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Abstract: | Analogues of characterizations of rank-preserving operators on field-valued matrices are determined for matrices witheentries in certain structures contained in the nonnegative reals. For example, if is the set of nonnegative members of a real unique factorization domain (e.g. the nonnegative reals or the nonnegative integers), M is the set of m×n matrices with entries in , and min(m,n)?4, then a “linear” operator on M preserves the “rank” of each matrix in M if and only if it preserves the ranks of those matrices in M of ranks 1, 2, and 4. Notions of rank and linearity are defined analogously to the field-valued concepts. Other characterizations of rank-preserving operators for matrices over these and other structures are also given. |
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