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
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author Song, Xiaofei
Zheng, Baodong
Cao, Chongguang
author_facet Song, Xiaofei
Zheng, Baodong
Cao, Chongguang
author_sort Song, Xiaofei
collection PubMed
description 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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spelling pubmed-38442232013-12-08 A Note on Decomposing a Square Matrix as Sum of Two Square Nilpotent Matrices over an Arbitrary Field Song, Xiaofei Zheng, Baodong Cao, Chongguang ScientificWorldJournal Research Article 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). Hindawi Publishing Corporation 2013-11-11 /pmc/articles/PMC3844223/ /pubmed/24319379 http://dx.doi.org/10.1155/2013/640350 Text en Copyright © 2013 Xiaofei Song et al. https://creativecommons.org/licenses/by/3.0/ This is an open access article distributed under the Creative Commons Attribution License, which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited.
spellingShingle Research Article
Song, Xiaofei
Zheng, Baodong
Cao, Chongguang
A Note on Decomposing a Square Matrix as Sum of Two Square Nilpotent Matrices over an Arbitrary Field
title A Note on Decomposing a Square Matrix as Sum of Two Square Nilpotent Matrices over an Arbitrary Field
title_full A Note on Decomposing a Square Matrix as Sum of Two Square Nilpotent Matrices over an Arbitrary Field
title_fullStr A Note on Decomposing a Square Matrix as Sum of Two Square Nilpotent Matrices over an Arbitrary Field
title_full_unstemmed A Note on Decomposing a Square Matrix as Sum of Two Square Nilpotent Matrices over an Arbitrary Field
title_short A Note on Decomposing a Square Matrix as Sum of Two Square Nilpotent Matrices over an Arbitrary Field
title_sort note on decomposing a square matrix as sum of two square nilpotent matrices over an arbitrary field
topic Research Article
url 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
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