广义半正定阵

Generalized positive semidefinite matrices

一个实的（未必对称）ｎ×ｎ矩阵Ａ称为广义半正定的，如果对任意非零的ｎ维列向量ｘ．均有正对角矩阵Ｄ＝Ｄ＿ｘ＞０，使ｘ￣ＴＤＡｘ≥０．讨论了广义正定矩阵的性质，给出了一个ｎ×ｎ分块矩阵为广义半正定阵的充要条件．

A real(may not symmetric) n ×n matrix M is said to be generalized positive semidefinite,if for any real nonzero n dimensional vector x,there exist D= Dz,such that xTDAx≥0. We give a necessary and sufficient condition for determining whether a patiitioned n ×n matrix is generalized positive semidefinite and property of generalizing positive definite.