特征值法求解二次型的条件最值问题

Applying Eigenvalues to Solve the Conditional Extremum of Quadrics Form

根据Lagrange乘数法求解条件最值问题的原理,针对特殊的二次型条件最值问题,分析最值与特征值间的对应关系,给出二次型条件最值问题求解的特征值方法,并结合例子说明特征值方法求解的简便及有效,具有一定的应用价值.

Based on Lagrange method of multipliers solving conditional extremum, for a certain conditional extremum of quadrics form, its extremums can be determined by the eigenvalues. The method of eigenvalues to solve conditional extremum is illustrated by some examples,which prove the method very convenient,effective and applicable.