报告人：魏木生 教授（上海师范大学）

时间：2018年3月14日(周三)上午10：00 -- 11：00

地点：闵行校区数学系102报告厅

主持人：潘建瑜 教授

报告简介：

Let $A$ be an arbitrary square matrix and its Jordan canonical form is $P^{-1}AP=J=\diag (J_1(\lambda_1),\cdots,J_q(\lambda_q))$ with $P$ an invertible matrix. $\lambda_1,\cdots,\lambda_q$ are different eigenvalues of matrix $A$. The commuting solution problem of the matrix equation $AXA=XAX$ is equivalent to the problem $J_i(\lambda_i)Y^{(i)}= Y^{(i)}J_i(\lambda_i), J_i(\lambda_i)^2$, $Y^{(i)}=J_i(\lambda_i) (Y^{(i)})^2$ with $Y=P^{-1}XP =\diag(Y^{(1)}, \cdots, Y^{(q)})$. We give the structures of the commuting solutions $Y^{(i)}$ in special Toeplitz forms. Based on them, we construct new matrices $H_\eta^{(\delta_1,\delta_2)}$ related to the commuting solutions. Then we proposea method of solving all the commuting Yang-Baxter-like solutions, by which all solutions can be obtained step by step by recursively solving matrix equations in two cases $\lambda_i=0$ or $\lambda_i\neq0$ with respect to the $i$-th Jordan block $J_i(\lambda_i)$..