A Note on Decomposing a Square Matrix as Sum of Two Square Nilpotent Matrices over an Arbitrary Field

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).

Detalles Bibliográficos
Autores principales: Song, Xiaofei, Zheng, Baodong, Cao, Chongguang
Formato: Online Artículo Texto
Lenguaje:English
Publicado: Hindawi Publishing Corporation 2013
Materias:
Research Article
Acceso en línea:https://www.ncbi.nlm.nih.gov/pmc/articles/PMC3844223/
https://www.ncbi.nlm.nih.gov/pubmed/24319379
http://dx.doi.org/10.1155/2013/640350
Descripción
Sumario: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).

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