Quasi-permutation singular matrices are products of idempotents

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• 作者：Adel Alahmadi^a ; ^{adelnife2@yahoo.com" class="auth_mail" title="E-mail the corresponding author} ; S.K. Jain^a ; ^b ; ^{jain@ohio.edu" class="auth_mail" title="E-mail the corresponding author} ; André ; Leroy^c ; ^{andre.leroy@univ-artois.fr" class="auth_mail" title="E-mail the corresponding author}
• 关键词：15A23 ; 15A33 ; 15A48
• 刊名：Linear Algebra and its Applications
• 出版年：2016
• 出版时间：1 May 2016
• 年：2016
• 卷：496
• 期：Complete
• 页码：487-495
• 全文大小：273 K

文摘

A matrix A∈M_n(R)$A\in M_n(R)$ with coefficients in any ring R is a quasi-permutation matrix if each row and each column has at most one nonzero element. It is shown that a singular quasi-permutation matrix with coefficients in a domain is a product of idempotent matrices. As an application, we prove that a nonnegative singular matrix having nonnegative von Neumann inverse (also known as generalized inverse) is a product of nonnegative idempotent matrices.