Solving the Yang-Baxter-like matrix equation for rank-two matrices

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• 作者：Duanmei Zhou^a ; ^{gzzdm2008@163.com" class="auth_mail" title="E-mail the corresponding author} ; Guoliang Chen^b ; ^{glchen@math.ecnu.edu.cn" class="auth_mail" title="E-mail the corresponding author} ; Jiu Ding^b ; ^c ; ^{jiudin@gmail.com" class="auth_mail" title="E-mail the corresponding author}
• 关键词：15A24 ; 15A18 ; 15A21
• 刊名：Journal of Computational and Applied Mathematics
• 出版年：2017
• 出版时间：15 March 2017
• 年：2017
• 卷：313
• 期：Complete
• 页码：142-151
• 全文大小：409 K

文摘

Let A=PQ^T$A=P{Q}^T$, where P$P$ and Q$Q$ are two n×2$n\times 2$ complex matrices of full column rank such that detQ^TP≠0$det{Q}^{T}P\ne 0$ and so 0$0$ is a semisimple eigenvalue of A$A$ with multiplicity n−2$n-2$. We solve the quadratic matrix equation AXA=XAX$AXA=XAX$ completely.