复合矩阵的Lwner偏序与特征值不等式

Lwner partial order and eigenvalue inequalities for compound matrices

讨论了存在Lwner偏序的两矩阵的k级复合矩阵的关系,并将复合矩阵与广义Schur补结合起来,研究矩阵广义Schur补的复合矩阵与复合矩阵广义Schur补之间的Lwner偏序,得到了Ck[(A*BA)/α]≤[Ck(A/α)]*Ck[B(β)′]Ck(A/α)等结果,并给出相关的特征值与奇异值不等式,推广和改进了近期的相关结果.

The Loewner partial order for compound matrices are considered. Combing generalized Schur complements with compound matrices, the Loewner partial order for compound matices of generalized Schur complements is studied. Some inequalities, such as Ck [ （ A^＊ BA ）/α ]≤[ Ck （ A/α ） ]^＊ Ck [ B （β′） ] Ck （A/α ） are obtained. Several eigenvalue inequalities of compound matrices are also offered, which generalize some recent results.