Linear preservers on triangular matrices

✍ Scribed by W.L. Chooi; M.H. Lim

• Publisher: Elsevier Science
• Year: 1998
• Tongue: English
• Weight: 780 KB
• Volume: 269
• Category: Article
• ISSN: 0024-3795
• DOI: 10.1016/s0024-3795(97)00069-4

✦ Synopsis

Let T,(F) denote the vector space of all n x n upper triangular matrices over a field F. We characterize those linear transformations T on T,,(F) that satisfy one of the following properties:

(1) T preserves rank one matrices;

(2) T preserves both singular and nonsingular matrices; (3) T is nonsingular and T(adj A