Lim, Ming Huat and Tan, Sin Chee (2010) Bijective linear maps on semimodules spanned by Boolean matrices of fixed rank. Linear Algebra And Its Applications, 433 (7). pp. 1365-1373.
Full text not available from this repository.Abstract
Let M(m,n) (B) be the semimodule of all m x n Boolean matrices where B is the Boolean algebra with two elements Let k be a positive integer such that 2 <= k <= min (m, n). Let B (m, n, k) denote the subsemimodule of M(m,n) (B) spanned by the set of all rank k matrices. We show that if T is a buective linear mapping on B (m, n, k), then there exist permutation matrices P and Q such that T (A) = PAQ for all A is an element of B (m, n, k) or m = n and T (A) = PA(l)Q for all A is an element of B (m, n, k) This result follows from a more general theorem we prove concerning the structure of linear mappings on B (m, n, k) that preserve bot h the weight of each matrix and rank one matrices of weight k(2) Here the weight of a Boolean matrix is the number of its non-zero entries (C) 2010 Elsevier Inc All rights reserved.
| Item Type: | Article |
|---|---|
| Funders: | UNSPECIFIED |
| Uncontrolled Keywords: | Boolean matrix; Bijective linear mapping; Rank preserver |
| Subjects: | Q Science > Q Science (General) |
| Depositing User: | Mr Faizal 2 |
| Date Deposited: | 12 Jan 2015 04:04 |
| Last Modified: | 04 Dec 2019 08:08 |
| URI: | http://eprints.um.edu.my/id/eprint/11892 |
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