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中文摘要：
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.
英文摘要：
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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