次正定复矩阵  

Metapositive definite complex matrix.

作　　者：郭华[1] 李庆玉[1] 

机构地区：[1]重庆工商大学理学院,重庆400067

出　　处：《重庆工商大学学报（自然科学版）》2006年第4期347-350,共4页Journal of Chongqing Technology and Business University:Natural Science Edition

摘　　要：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.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 ,4 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.

关 键 词：次转置矩阵 次正定Hermite矩阵 次正定复矩阵 次特征值 

分 类 号：O151.21[理学—数学]