二次型极值及其推广的几个结论

Some Propositions on the Extreme Value of Quadratic Form

讨论了二次型在单位球面及其闭子集上的极值问题 ,并引入广义二次型的概念 ,利用正交变换从两个方面推广了二次型的极值与其对应的特征值之间的关系 .

The extreme value of quadratic form on a unit sphere and its closed sets are discussed in this paper.By introducing the extended quadratic form,and by use of orthogonal transform,a more general relation between the extreme value and the eigenvalue of the quadratic form is obtained.