Sign idempotent sign pattern matrices that allow idempotence

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• 作者：Sang-Gu Lee^a ; ^{sglee@skku.edu" class="auth_mail" title="E-mail the corresponding author} ; Jin-Woo Park^b ; ^{a0417001.paper@gmail.com" class="auth_mail" title="E-mail the corresponding author}
• 关键词：05A10 ; 05A19
• 刊名：Linear Algebra and its Applications
• 出版年：2015
• 出版时间：15 December 2015
• 年：2015
• 卷：487
• 期：Complete
• 页码：232-241
• 全文大小：282 K

文摘

It is well known that not all sign idempotent sign pattern matrices allow idempotence. In this paper, we found a necessary and sufficient condition for a sign idempotent sign pattern matrix to allow idempotence. In addition, we investigated the nonnegativity of sign idempotent sign pattern matrices that allow idempotence. Finally, we show that if A is a sign idempotent sign pattern matrix, then A   allows idempotence if and only if |A|=[|a_ij|]$|A|=[|a_{ij}|]$ also allows idempotence.