关于Hermite矩阵Schur补的迹的几个不等式

Several inequalities about the trace of Schur complement of Hermite matrix

利用Schur补的理论知识和Hermite矩阵的迹的不等式,研究了Hermite矩阵Schur补的迹的不等式的遗传性质,得到了Hermite矩阵Schur补的迹的Minkowski不等式、Holder不等式以及其他形式的不等式,并给出了理论证明,为处理大规模的矩阵计算提供了理论支撑。

By using the theoretical knowledge of Schur complement and the inequalities about the trace of H ermite matrix, the genetic properties of the inequalities about the trace of Sehur complement of Hermite matrix are investigated. Minkowski in- equality, Holder inequality and other inequalities about the trace of Schur complement of Hermite matrix are obtained and proved in the theory. They provide the theoretical support for dealing with the large-scale matrix calculation.