Additive preservers of rank-additivity on matrix spaces

CHOOI, W and LIM, M (2005) Additive preservers of rank-additivity on matrix spaces. Linear Algebra and its Applications, 402. pp. 291-302. ISSN 00243795

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Official URL: http://dx.doi.org/10.1016/j.laa.2005.01.020

Abstract

Let F be a field. Let V denote the vector space of all m x n matrices over F or the vector space of all n x n symmetric matrices over F of characteristic not 2 or 3. For each fixed positive integer s >= 2, let Qs denote the set of all matrix pairs (A, B) in V such that rank(A + B) = rank(A) + rank(B) <= s. We characterize additive mappings psi on V such that (psi(A), psi (B)) epsilon Qs whenever (A, B) epsilon Qs for a fixed s. We also describe the structure of linear mappings from the space of n x n matrices over F to the space of p x q matrices over F that preserve rank-additivity, where char F not equal 2. (c) 2005 Elsevier Inc. All rights reserved.

Item Type: Article
Subjects: Q Science > QA Mathematics
Divisions: Faculty of Engineering (FOE)
Depositing User: Ms Rosnani Abd Wahab
Date Deposited: 12 Aug 2011 01:33
Last Modified: 12 Aug 2011 01:33
URI: http://shdl.mmu.edu.my/id/eprint/2229

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