Explicit solutions of the Yang-Baxter-like matrix equation for an idempotent matrix

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• 作者：Saeed Ibrahim Adam Mansour ^{mansour@uofk.edu" class="auth_mail" title="E-mail the corresponding author} ; Jiu Ding ; ^{Jiu.Ding@usm.edu" class="auth_mail" title="E-mail the corresponding author} ; Qianglian Huang ^{huangql@yzu.edu.cn" class="auth_mail" title="E-mail the corresponding author}
• 关键词：Yang&ndash ; Baxter-like matrix equation ; Idempotent matrix
• 刊名：Applied Mathematics Letters
• 出版年：2017
• 出版时间：January 2017
• 年：2017
• 卷：63
• 期：Complete
• 页码：71-76
• 全文大小：480 K

文摘

Let d="mmlsi1" class="mathmlsrc">data-mathURL="/science?_ob=MathURL&_method=retrieve&_eid=1-s2.0-S0893965916302154&_mathId=si1.gif&_user=111111111&_pii=S0893965916302154&_rdoc=1&_issn=08939659&md5=a09baec398d93cf2051e4b7a7c7c2f97" title="Click to view the MathML source">Adden">de">$A$ be an idempotent matrix. We obtain an explicit expression for all the solutions of the quadratic matrix equation d="mmlsi2" class="mathmlsrc">data-mathURL="/science?_ob=MathURL&_method=retrieve&_eid=1-s2.0-S0893965916302154&_mathId=si2.gif&_user=111111111&_pii=S0893965916302154&_rdoc=1&_issn=08939659&md5=3b6e3f819f3a00271749f99cbd1031ba" title="Click to view the MathML source">AXA=XAXdden">de">$AXA=XAX$, completing the task of finding general solutions of the equation explicitly with a given idempotent matrix d="mmlsi1" class="mathmlsrc">data-mathURL="/science?_ob=MathURL&_method=retrieve&_eid=1-s2.0-S0893965916302154&_mathId=si1.gif&_user=111111111&_pii=S0893965916302154&_rdoc=1&_issn=08939659&md5=a09baec398d93cf2051e4b7a7c7c2f97" title="Click to view the MathML source">Adden">de">$A$.