关于分块半正定矩阵的Everitt不等式的注记

Characterizationon Everitt Inequality of Partitioned Semi-positive Definite Matrices

在矩阵分析中,分块半正定矩阵是一类具有较好性质的矩阵。分块半正定矩阵相关的理论研究一般都是从2×2分块半正定矩阵开始,因此2×2分块半正定矩阵性质的研究是矩阵分析中基本的研究课题之一。鉴于此,基于已有的分块半正定矩阵的相关性质,通过2×2分块半正定矩阵来研究分块半正定矩阵行列式的Everitt不等式。利用矩阵分块的技巧,文章不仅给出了它的一个新的证明,同时给出了等号成立的一个新的刻画。

In matrix analysis,the partitioned semi-positive definite matrices is a kind of matrices with excellent pro-perties.The theoretical research on partitioned semi-positive definite matrices generally begins with 2×2 partitioned semi-positive definite matrices.Therefore,the study of the properties of 2×2 partitioned semi-positive definite matrices is one of the basic research topics in matrix analysis.In view of this,based on the properties of existing partitioned semi-positive definite matrices,this paper studies the Everitt inequality of determinant of partitioned semi-positive definite matrices by 2×2 partitioned semi-positve definite matrices.Using the technique of matrix partition,this paper not only gives a new proof of it,but also gives a new characterization of the equality sign.