分块Hermite阵与斜Hermite阵的最大秩与最小秩  

Extremal ranks for block Hermitian and skew-Hermitian matrices

作　　者：张凤霞[1] 李莹[1,2] 郭文彬[1] 赵建立[1] 

机构地区：[1]聊城大学数学科学学院,山东聊城252059 [2]上海理工大学管理学院,上海200093

出　　处：《山东大学学报（理学版）》2010年第4期106-110,共5页Journal of Shandong University(Natural Science)

基　　金：国家自然科学基金资助项目(10771073)

摘　　要：利用有关Hermite阵、斜Hermite阵的几个表达式的秩与分块矩阵的性质,研究了分块Hermite阵[ABB*X]在无其他约束条件和满足约束条件BXB*=A(A=A*)下的最大秩与最小秩,与分块斜Hermite阵[ABB*X]在无约束条件和满足约束条件BXB*=A(A=-A*)下的最大秩与最小秩。In this paper,by using the ranks of several expressions about Hermitian matrices and skew-Hermitian matrices and the characters of block matrices,the maximal ranks and minimal ranks of the block Hermitian matrix（ABBX） with respect to X are investigated,where X is an arbitrary Hermitian matrices or X is the Hermitian solutions to the matrix equation BXB=A（A=A）.And the maximal ranks and minimal ranks of the block skew-Hermitian matrix （AB-BX） with respect to X are investigated,where X is an arbitrary skew-Hermitian matrix or X is the skew-Hermitian solutions to the matrix equation BXB=A（A=-A）.

关 键 词：分块Hermite阵 分块斜Hermite阵 最大秩 最小秩 

分 类 号：O151.21[理学—数学]