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On linear operators strongly preserving invariants of Boolean matrices |
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| Authors: | Yizhi Chen Xianzhong Zhao |
| Affiliation: | 1. Department of Mathematics Northwest University, Xi’an, Shaanxi, 710127, China 2. Department of Mathematics, Huizhou University, Huizhou, Guangdong, 516007, P.R.China 3. College of Mathematics and Information Science, Jiangxi Normal University, Nanchang, Jiangxi, 330022, P.R.China |
| Abstract: | Let U k be the general Boolean algebra and T a linear operator on M m,n (U k ). If for any A in M m,n (U k ) (M n (U k ), respectively), A is regular (invertible, respectively) if and only if T(A) is regular (invertible, respectively), then T is said to strongly preserve regular (invertible, respectively) matrices. In this paper, we will give complete characterizations of the linear operators that strongly preserve regular (invertible, respectively) matrices over U k . Meanwhile, noting that a general Boolean algebra U k is isomorphic to a finite direct product of binary Boolean algebras, we also give some characterizations of linear operators that strongly preserve regular (invertible, respectively) matrices over 169-7 k from another point of view. |
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