广义半正定矩阵

Generalized Positive Semidefinite Matrices

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.