|
\(不难求出其行列式为a_{11}a_{22}-a_{12}a_{21}=\lambda_{1}\lambda_{2}\)
\(由对称可知,a_{12}=a_{21},且trace(A)=a_{11}+a_{22}=\lambda_{1}+\lambda_{2},\)
\(那么就有a_{12}^{2}=a_{11}a_{22}-\lambda_{1}\lambda_{2}≤(\dfrac {\lambda_{1}+\lambda_{2}}{2})^{2}-\lambda_{1}\lambda_{2}=37^{2},\)
\(当且仅当a_{11}=a_{22}=1986时取等,故a_{12}最大值[I]=37\) |
|