分块矩阵的保半正定性  

The Preserver Problems of Positive Semi-definite Block Matrix

作　　者：张萍萍 任芳国[1] ZHANG Pingping;REN Fangguo(School of Mathematics and Information Science,Shaanxi Normal University,Xi'an 710062,Shaanxi,China)

机构地区：[1]陕西师范大学数学与信息科学学院

出　　处：《咸阳师范学院学报》2019年第6期10-12,共3页Journal of Xianyang Normal University

基　　金：国家自然科学基金项目(11471200)

摘　　要：研究了2×2半正定Hermite分块矩阵的保半正定性的问题。利用半正定Hermite矩阵的等价条件和2×2分块Hermite矩阵的性质,得到了当A为半正定Hermite分块矩阵时,则对每一子块分别求谱半径、谱跨度后所成的矩阵仍为半正定矩阵。The problem of maintaining semi-definiteness of two by two semi-definite Hermite block matrix was presented in this paper.By using the conditions of equivalence of semi-definite Hermite block matrix and properties of two by two Hermite block matrix,we get if A is a positive semi-definite Hermite block matrix,the resulting matrix that is taken the spectral radius,spectrum span for every block matrix respectively are still a positive semi-definite block matrix.

关 键 词：分块半正定矩阵 谱半径 谱跨度 

分 类 号：O151.21[理学—数学]