Projection-based commuting solutions of the Yang-Baxter matrix equation for non-semisimple eigenvalues

详细信息    查看全文

• 作者：Qixiang Dong ^{qxdongyz@outlook.com" class="auth_mail" title="E-mail the corresponding author}
• 关键词：Matrix equation ; Jordan matrix ; Jordan blocks ; Projection
• 刊名：Applied Mathematics Letters
• 出版年：2017
• 出版时间：February 2017
• 年：2017
• 卷：64
• 期：Complete
• 页码：231-234
• 全文大小：647 K

文摘

Let dfdc4904684b5a9" title="Click to view the MathML source">A$A$ be a square matrix. We construct projection-based commuting solutions of the quadratic matrix equation AXA=XAX$AXA=XAX$, which are associated with non-semisimple eigenvalues of dfdc4904684b5a9" title="Click to view the MathML source">A$A$ with at least one 1×1$1\times 1$ Jordan block, based on special projections onto some subspaces of the corresponding generalized eigenspaces. The result extends the main one (Ding, Zhang, 2014) from the semisimple eigenvalue case to the non-semisimple one.