矩阵的保半正定性  

The preserver problems of positive semidefinite matrix

作　　者：秦晓燕[1] 任芳国[1] 

机构地区：[1]陕西师范大学数学与信息科学学院,陕西西安710062

出　　处：《纺织高校基础科学学报》2011年第3期403-405,共3页Basic Sciences Journal of Textile Universities

基　　金：国家自然科学基金资助项目(10971123);陕西师范大学重点基金资助项目(995281)

摘　　要：利用经典的半正定Hermite矩阵的等价条件,讨论了2×2分块矩阵的保半正定性问题.A为2×2半正定Hermite分块矩阵时,则对每一子块分别取迹、行列式、谱范数、秩、数值域后所成矩阵仍为半正定;当A为2×2分块矩阵时,的范数和数值域半径分别不超过的范数和数值域半径.By using the classical conditions of equivalence of semidefinite Hermite block matrix sufficiently,the problem of maintaining semidefiniteness with two by two block matrix are mainly discussed.Firstly,if A∈Mn is a positive semidefinite Hermite block matrix,the resulting matrix that is taken trace,determinant,spectrum norm,rank and numerical radius for every block matrix respectively is still positive semidefinite.Secondly,if A∈Mn is a block matrix,the norm and numerical radius of A are not exceeded that of .

关 键 词：半正定矩阵 压缩矩阵 谱范数 

分 类 号：O151.21[理学—数学]