title: A note on decomposing a square matrix as sum of two square nilpotent matrices over an arbitrary field.
abstract: Let K be an arbitrary field and X a square matrix over K. Then X is sum of two square nilpotent matrices over K if and only if, for every algebraic extension L of K and arbitrary nonzero α ∈ L, there exist idempotent matrices P 1 and P 2 over L such that X = αP 1 - αP 2.
authors: Department of Mathematics, Harbin Institute of Technology, Harbin 150001, China.
authors: Xiaofei
authors: X
authors: Song
authors: Baodong
authors: B
authors: Zheng
authors: Chongguang
authors: C
authors: Cao
mesh_terms: D000465:Algorithms; D003198:Computer Simulation; D008433:Mathematics; D008962:Models, Theoretical; D009716:Numerical Analysis, Computer-Assisted