一个求特征值的问题
今天13级数院的JJ发来提问:
求对称矩阵
\[A = \left( {\begin{array}{*{20}{c}}{a_{11}^2}&{{a_{11}}{a_{12}} + 1}&{{a_{11}}{a_{13}} + 1}& \cdots &{{a_{11}}{a_{1n}} + 1}\\{{a_{11}}{a_{12}} + 1}&{a_{22}^2}&{{a_{22}}{a_{23}} + 1}& \cdots &{{a_{22}}{a_{2n}} + 1}\\{{a_{11}}{a_{13}} + 1}&{{a_{22}}{a_{23}} + 1}& \ddots & \ddots & \vdots \\\vdots & \vdots & \ddots &{a_{n - 1,n - 1}^2}&{{a_{n - 1,n - 1}}{a_{n - 1,n}} + 1}\\{{a_{11}}{a_{1n}} + 1}&{{a_{22}}{a_{2n}} + 1}& \cdots &{{a_{n - 1,n - 1}}{a_{n - 1,n}} + 1}&{a_{nn}^2}\end{array}} \right)\]的特征值.
