摘要
在本文中(1)证明了参考文献[2]与[3]中所定义的两类广义正定矩阵的逆仍是同种类型的广义正定矩阵;(2)给出了参考文献[2]中广义正定矩阵的行列式满足如下不等式|A|≤a_(n n)P_(n-1)这里P_(n-1)是A的n-1阶顺序主子式.进一步有|A|≤a_(n n)a_(n-1 n-1)…a_(22)a_(11)
In this paper first we have proved that the inverses of generalized positive definite matrices in Reference [ 2] &[3]are also same kinds of generalized positive definite matrices; second the determinants of generalized positive definite matrice in Reference [ 2 ] which we have given satisfy the following inequality| A |≤annPn-1where Pn-1 is sequential principal minor determinant. Furthermore we have | A|≤annan-1 n-1… a22a11.
关键词
广义正定矩阵
逆
行列式
矩阵
generalized positive definite matrices
sequential principal minor
inverse of matrices
determinant
