为了简化大型行(列)酉对称矩阵的极分解, 研究了酉对称矩阵的性质, 获得了一些新的结果, 给出了酉对称矩阵的极分解和广义逆的公式, 它们可极大地减少行(列)酉对称矩阵的极分解的计算量与存储量, 并且不会丧失数值精度.同时对酉对称矩阵的极分解作了扰动分析.

To simplify the polar factorization of row (column) unitary symmetric matrix, the properties of row (column) unitary symmetric matrix were studied, and some new results were gained. The formula of the polar factorization and generalized inverse of row (column) unitary symmetric matrix were obtained, all of which can draatically reduce the aount of calculation and polar factorization of row (column) unitary symmetric matrix can dramatically save the CPU time and memory without losing any numerical precision. Some perturbation bounds of the polar factor were presented.