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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.
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Basic Information:
China Classification Code:O151.21
Citation Information:
[1]DU Juan,FENG Si-chen,TAN Ren-jun(College of Information Management,Chengdu University of Technology,Chengdu 610059,China).Decomposition of Symmetry Full Rank Matrices on Complex Matrix[J].Journal of Zhengzhou University(Natural Science Edition),2011,43(01):4-6+10.
Fund Information:
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
2011-03-15
2011-03-15