矩阵秩的Sylvester不等式

Sylvester Inequality about the Rank of Matrix

本文利用矩阵秩的性质和分块矩阵运算技巧对Sylvester不等式进行了研究,给出了等号成立的充要条件,将其做了一定程度的推广,并得到了一些方便应用的充分条件,丰富了矩阵秩的性质。

Using the property of the rank of matrix and the operation skill of block matrices,the Sylvester inequality is studied in this paper,which gives the necessary and sufficient conditions for the equal sign to hold,generalizes it to a certain extent,and obtains some concrete sufficient conditions for convenient application. The result enriches the properties of the rank of matrix.