行(列)对称矩阵的奇异值分解

Singular Value Decomposition of Row(Column) Symmetric Matrix

提出了行(列)转置矩阵的概念,研究了行(列)转置矩阵与行(列)对称矩阵的性质,获得了一些新的结果.给出了行(列)对称矩阵的奇异值分解的公式,它们可极大地减少行(列)对称矩阵的奇异值分解的计算量与存储量,而且不会降低数值精度.

The concept of row （column） transposed matrix is proposed, and the basic properties of the row （column） transposed matrix and row （column） symmetric matrix are analyzed, which leads to some new results. In addition, the formula of the singular value decomposition of row （column） symmetric matrix is given, which makes the calculation easy and accurate, and saves the CPU time and memory dramatically without loss of any numerical precision.