复矩阵的对称满秩分解  

Decomposition of Symmetry Full Rank Matrices on Complex Matrix

作　　者：杜鹃[1] 冯思臣[1] 谭仁俊[1] 

机构地区：[1]成都理工大学信息管理学院,四川成都610059

出　　处：《郑州大学学报（理学版）》2011年第1期4-6,10,共4页Journal of Zhengzhou University:Natural Science Edition

基　　金：国家自然科学基金资助项目;编号10471112;四川省教育厅自然科学基金资助项目;编号08ZA144

摘　　要：在矩阵的正交三角分解、奇异值分解的基础上,给出了复矩阵的Hermite标准形的求解方法,得到了将复矩阵分解为一个酉矩阵和Hermite半正定矩阵的乘积,以及分解为满秩矩阵与幂等矩阵之乘积的方法.证明了复方阵可分解为一个复对称矩阵与一个复对称满秩矩阵之积.进一步给出了复满秩阵分解为两个Hermite酉矩阵与正定阵之积的方法.Based on the orthogonal triangular decomposition and singular value decomposition of a real matrix,the algorithm solving the Hermite standard form of a complex matrix was presented.The decompositions of a complex matrix into the product of a unitary matrix and a Hermite semi-positive matrix were presented.And the product of a full rank matrix and an idempotent matrix were presented too.It was proved that a complex square matrix could be decomposed into the product of a symmetric matrices,and a symmetric full rank matrix.Moreover,it was put forward that the algorithm on decomposing a complex full rank matrix into the product of a positive matrix and two Hermite unitary matrices.

关 键 词：满秩矩阵 复矩阵分解 酉分解 QR分解 

分 类 号：O151.21[理学—数学]