科研之友
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摘要
The Boolean rank of a nonzero m x n Boolean matrix A is the least integer k such that there are an m x k Boolean matrix B and a k x n Boolean matrix C with A = BC. We investigate the structure of linear transformations T : M-m,M-n -> M-p,M-q which preserve Boolean rank. We also show that if a linear transformation preserves the set of Boolean rank 1 matrices and the set of Boolean rank k matrices for any k, 2 <= k <= min{m, n} (or if T strongly preserves the set of Boolean rank 1 matrices), then T preserves all Boolean ranks.
- 出版日期2015-5
