次正定复矩阵

研究了复矩阵的次正定性的性质和一系列充分必要条件,得到了“n阶次正定复矩阵的次特征值实部为正”与“当JA为复正规矩阵时,A是次正定复矩阵的充分必要条件是A的次特征值实部为正”等结论;讨论并给出了矩阵乘积是次正定复矩阵的充分和充要条件;得到了与著名的Ostrowski-Taussky不等式、Hadamard不等式、Oppenhein不等式等相应的重要结果.

Metapositive definite complex matrix.

The properties of metapositive definite complex matrices and a group of sufficiencies as well are discussed.This paper includes theorems such as the one that the real parts of the sub-characteristic values belonged to an n-square metapositive definite complex matrix are positive,and that if JA is a normal composite matrix,then A is a metapositive definite complex matrix if and only if the real part of the sub-characteristic value belonged to A is real.In addition,the paper proves the sufficiencies and necessities of the problem that the production of two matrices is a metapositive definite complex matrix.