Additive preservers of rank-additivity on matrix spaces

✍ Scribed by Wai-Leong Chooi; Ming-Huat Lim

• Publisher: Elsevier Science
• Year: 2005
• Tongue: English
• Weight: 230 KB
• Volume: 402
• Category: Article
• ISSN: 0024-3795
• DOI: 10.1016/j.laa.2005.01.020

✦ Synopsis

Let F be a field. Let V denote the vector space of all m × n matrices over F or the vector space of all n × n symmetric matrices over F of characteristic not 2 or 3. For each fixed positive integer s 2, let Q s 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 ψ on V such that (ψ(A), ψ(B)) ∈ Q s whenever (A, B) ∈ Q s for a fixed s. We also describe the structure of linear mappings from the space of n × n matrices over F to the space of p × q matrices over F that preserve rank-additivity, where char F / = 2.