广义半正定矩阵  

Generalized Positive Semidefinite Matrices

作　　者：赵志新[1] 石澄贤[1] 

机构地区：[1]江苏石油化工学院基础课部

出　　处：《江苏石油化工学院学报》1998年第4期55-57,共3页Journal of Jiangsu Institute of Petrochemical Technology

摘　　要：一个实的（未必对称）ｎ×ｎ矩阵Ａ称为广义半下定的，如果对任意非零的ｎ维向量ｘ，均有正对角矩阵Ｄ＝Ｄｘ＞０，使ｘＴＤＡｘ≥０。证明了当Ａ、Ｂ分别为ｍ阶，ｎ阶广义半正定矩阵，则ＡＳ（Ｄ２Ｂ）及ＡＳ（ＤＢ）亦是。同时也讨论了广义半正定矩阵行列式的几个不等式。A real (perhaps not symmetric) n × n matrix A is said to be generalized positive semidefinite,if for any real nonzero n dimensional vector x ,there exist D=D X,such that x T DAx ≥0.We proved that AS(DB) and AS(DB) are generalized positive semidefinite matrix if A B are generalized positive semidefinite matrix and determinant inequality of generalized positive definite matrices.

关 键 词：广义半正定阵 矩阵 

分 类 号：O151.21[理学—数学]