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 ce?_ob=MathURL&_method=retrieve&_eid=1-s2.0-S0377042716304277&_mathId=si1.gif&_user=111111111&_pii=S0377042716304277&_rdoc=1&_issn=03770427&md5=35d87f1be618af889e255fb56f0d5dde" title="Click to view the MathML source">A=PQ^T$A=P{Q}^T$, where ce?_ob=MathURL&_method=retrieve&_eid=1-s2.0-S0377042716304277&_mathId=si2.gif&_user=111111111&_pii=S0377042716304277&_rdoc=1&_issn=03770427&md5=da9297ac1ebfb25e8a0ee63334d7d41b" title="Click to view the MathML source">P$P$ and ce?_ob=MathURL&_method=retrieve&_eid=1-s2.0-S0377042716304277&_mathId=si3.gif&_user=111111111&_pii=S0377042716304277&_rdoc=1&_issn=03770427&md5=2d80b83ef70107d5f60a37195a91a27d" title="Click to view the MathML source">Q$Q$ are two ce?_ob=MathURL&_method=retrieve&_eid=1-s2.0-S0377042716304277&_mathId=si4.gif&_user=111111111&_pii=S0377042716304277&_rdoc=1&_issn=03770427&md5=96213d9bb963a0c4c8830018272eeeac" title="Click to view the MathML source">n×2$n\times 2$ complex matrices of full column rank such that ce?_ob=MathURL&_method=retrieve&_eid=1-s2.0-S0377042716304277&_mathId=si5.gif&_user=111111111&_pii=S0377042716304277&_rdoc=1&_issn=03770427&md5=6a8bc4ac911c44664ffda0753dda8276" title="Click to view the MathML source">detQ^TP≠0$det{Q}^{T}P\ne 0$ and so ce?_ob=MathURL&_method=retrieve&_eid=1-s2.0-S0377042716304277&_mathId=si6.gif&_user=111111111&_pii=S0377042716304277&_rdoc=1&_issn=03770427&md5=4ce2395c47c321907ce67590b78c385f" title="Click to view the MathML source">0$0$ is a semisimple eigenvalue of ce?_ob=MathURL&_method=retrieve&_eid=1-s2.0-S0377042716304277&_mathId=si7.gif&_user=111111111&_pii=S0377042716304277&_rdoc=1&_issn=03770427&md5=81eeaa9c43f9d5655d1312922241e19b" title="Click to view the MathML source">A$A$ with multiplicity ce?_ob=MathURL&_method=retrieve&_eid=1-s2.0-S0377042716304277&_mathId=si8.gif&_user=111111111&_pii=S0377042716304277&_rdoc=1&_issn=03770427&md5=47440d4580b7deb9a6b7bcc9ae6a2d38" title="Click to view the MathML source">n−2$n-2$. We solve the quadratic matrix equation ce?_ob=MathURL&_method=retrieve&_eid=1-s2.0-S0377042716304277&_mathId=si9.gif&_user=111111111&_pii=S0377042716304277&_rdoc=1&_issn=03770427&md5=e86da31638a86b0f9f75e79290611bed" title="Click to view the MathML source">AXA=XAX$AXA=XAX$ completely.